Balbharati solutions for Mathematics and Statistics 1 (Arts and Science) [English] 11 Standard Maharashtra State Board chapter 5 - Straight Line [Latest edition]

If A(1, 3) and B(2, 1) are points, find the equation of the locus of point P such that PA = PB.

A(−5, 2) and B(4, 1). Find the equation of the locus of point P, which is equidistant from A and B

If A(2, 0) and B(0, 3) are two points, find the equation of the locus of point P such that AP = 2BP.

If A(4, 1) and B(5, 4), find the equation of the locus of point P if PA² = 3PB² 

A(2, 4) and B(5, 8), find the equation of the locus of point P such that PA² − PB² = 13

A(1, 6) and B(3, 5), find the equation of the locus of point P such that segment AB subtends right angle at P. (∠APB = 90°)

If the origin is shifted to the point O′(2, 3), the axes remaining parallel to the original axes, find the new co-ordinates of the point A(1, 3)

If the origin is shifted to the point O′(2, 3), the axes remaining parallel to the original axes, find the new coordinates of the point B(2, 5)

If the origin is shifted to the point O′(1, 3) the axes remaining parallel to the original axes, find the old coordinates of the point C(5, 4)

If the origin is shifted to the point O′(1, 3) the axes remaining parallel to the original axes, find the old coordinates of the point D(3, 3)

If the co-ordinates A(5, 14) change to B(8, 3) by shift of origin, find the co-ordinates of the point where the origin is shifted

Obtain the new equation of the following loci if the origin is shifted to the point O'(2, 2), the direction of axes remaining the same:

3x − y + 2 = 0

Obtain the new equation of the following loci if the origin is shifted to the point O'(2, 2), the direction of axes remaining the same:

x² + y² – 3x = 7

Obtain the new equation of the following loci if the origin is shifted to the point O'(2, 2), the direction of axes remaining the same:

xy − 2x − 2y + 4 = 0

Obtain the new equation of the following loci if the origin is shifted to the point O'(2, 2), the direction of axes remaining the same:

y² − 4x − 4y + 12 = 0

Find the slope of the following line which passes through the points:

A(2, −1), B(4, 3)

Find the slope of the following line which passes through the points:

C(−2, 3), D(5, 7)

Find the slope of the following line which passes through the points:

E(2, 3), F(2, −1)

Find the slope of the following line which passes through the points:

G(7, 1), H(−3, 1)

If the X and Y-intercepts of lines L are 2 and 3 respectively then find the slope of line L.

Find the slope of the line whose inclination is 30°

Find the slope of the line whose inclination is `pi/4`

A line makes intercepts 3 and 3 on the co-ordinate axes. Find the inclination of the line.

Without using Pythagoras theorem show that points A(4, 4), B(3, 5) and C(−1, −1) are the vertices of a right angled triangle.

Find the slope of the line which makes angle of 45° with the positive direction of the Y-axis measured anticlockwise

Find the value of k for which points P(k, −1), Q(2, 1) and R(4, 5) are collinear.

Find the acute angle between the X-axis and the line joining points A(3, −1) and B(4, −2).

A line passes through points A(x₁, y₁) and B(h, k). If the slope of the line is m then show that k − y₁ = m(h − x₁)

If points A(h, 0), B(0, k) and C(a, b) lie on a line then show that `"a"/"h" + "b"/"k"` = 1

Write the equation of the line :

parallel to the X−axis and at a distance of 5 unit form it and above it

Write the equation of the line :

parallel to the Y−axis and at a distance of 5 unit form it and to the left of it

Write the equation of the line :

parallel to the X-axis and at a distance of 4 unit form the point (−2, 3)

Obtain the equation of the line :

parallel to the X−axis and making an intercept of 3 unit on the Y−axis

Obtain the equation of the line :

parallel to the Y−axis and making an intercept of 4 unit on the X−axis

Obtain the equation of the line containing the point :

A(2, – 3) and parallel to the Y−axis

Obtain the equation of the line containing the point :

B(4, –3) and parallel to the X-axis

Find the equation of the line passing through the points A(2, 0), and B(3, 4)

Find the equation of the line passing through the points P(2, 1) and Q(2, –1)

Find the equation of the line containing the origin and having inclination 60°

Find the equation of the line passing through the origin and parallel to AB, where A is (2, 4) and B is (1, 7)

Find the equation of the line having slope `1/2` and containing the point (3, −2).

Find the equation of the line containing point A(3, 5) and having slope `2/3`.

Find the equation of the line containing point A(4, 3) and having inclination 120°

Find the equation of the line passing through the origin and which bisects the portion of the line 3x + y = 6 intercepted between the co-ordinate axes.

Line y = mx + c passes through points A(2, 1) and B(3, 2). Determine m and c.

Find the equation of the line having inclination 135° and making X-intercept 7

The vertices of a triangle are A(3, 4), B(2, 0), and C(−1, 6). Find the equation of the line containing side BC.

The vertices of a triangle are A(3, 4), B(2, 0), and C(−1, 6). Find the equation of the line containing the median AD

The vertices of a triangle are A(3, 4), B(2, 0), and C(−1, 6). Find the equation of the line containing the midpoints of sides AB and BC

Find the x and y intercept of the following line:

`x/3 + y/2` = 1

Find the x and y intercept of the following line:

`(3x)/2 + (2y)/3` = 1

Find the x and y intercept of the following line:

2x − 3y + 12 = 0

Find equations of lines which contains the point A(1, 3) and the sum of whose intercepts on the coordinate axes is zero.

Find equations of lines containing the point A(3, 4) and making equal intercepts on the co-ordinates axes.

Find equations of altitudes of the triangle whose vertices are A(2, 5), B(6, –1) and C(–4, –3).

Find the equations of perpendicular bisectors of sides of the triangle whose vertices are P(−1, 8), Q(4, −2), and R(−5, −3)

Find the coordinates of the orthocenter of the triangle whose vertices are A(2, −2), B(1, 1), and C(−1, 0).

N(3, −4) is the foot of the perpendicular drawn from the origin to line L. Find the equation of line L.

Find the slope, X-intercept, Y-intercept of the following line:

2x + 3y – 6 = 0

Find the slope, X-intercept, Y-intercept of the following line:

3x − y − 9 = 0

Find the slope, X-intercept, Y-intercept of the following line:

x + 2y = 0

Write the following equation in ax + by + c = 0 form.

y = 2x – 4

Write the following equation in ax + by + c = 0 form.

y = 4

Write the following equation in ax + by + c = 0 form.

`x/2 + y/4` = 1

Write the following equation in ax + by + c = 0 form.

`x/3 - y/2` = 0

Show that lines x – 2y – 7 = 0 and 2x − 4y + 15 = 0 are parallel to each other

Show that lines x − 2y − 7 = 0 and 2x + y + 1 = 0 are perpendicular to each other. Find their point of intersection

If the line 3x + 4y = p makes a triangle of area 24 square unit with the co-ordinate axes then find the value of p.

Find the co-ordinates of the foot of the perpendicular drawn from the point A(–2, 3) to the line 3x – y – 1 = 0

Find the co-ordinates of the circumcenter of the triangle whose vertices are A(–2, 3), B(6, –1), C(4, 3).

Find the co-ordinates of the orthocenter of the triangle whose vertices are A(3, –2), B(7, 6), C(–1, 2).

Show that lines 3x − 4y + 5 = 0, 7x − 8y + 5 = 0, and 4x + 5y − 45 = 0 are concurrent. Find their point of concurrence

Find the equation of the line whose X-intercept is 3 and which is perpendicular to the line 3x − y + 23 = 0.

Find the distance of the origin from the line 7x + 24y – 50 = 0

Find the distance of the point A(−2, 3) from the line 12x − 5y − 13 = 0 

Find the distance between parallel lines 4x − 3y + 5 = 0 and 4x − 3y + 7 = 0

Find the distance between parallel lines 9x + 6y − 7 = 0 and 3x + 2y + 6 = 0

Find points on the line x + y − 4 = 0 which are at one unit distance from the line 4x + 3y – 10 = 0.

Find the equation of the line parallel to the X-axis and passing through the point of intersection of lines x + y − 2 = 0 and 4x + 3y = 10

Find the equation of the line passing through the point of intersection of lines x + y − 2 = 0 and 2x − 3y + 4 = 0 and making intercept 3 on the X-axis

If A(4, 3), B(0, 0), and C(2, 3) are the vertices of ∆ABC then find the equation of bisector of angle BAC.

D(−1, 8), E(4, −2), F(−5, −3) are midpoints of sides BC, CA and AB of ∆ABC Find equations of sides of ∆ABC

D(−1, 8), E(4, −2), F(−5, −3) are midpoints of sides BC, CA and AB of ∆ABC Find co-ordinates of the circumcenter of ΔABC

O(0, 0), A(6, 0) and B(0, 8) are vertices of a triangle. Find the co-ordinates of the incenter of ∆OAB

Select the correct option from the given alternatives:

If A is (5, −3) and B is a point on the x-axis such that the slope of line AB is −2 then B ≡

Select the correct option from the given alternatives:

If the point (1, 1) lies on the line passing through the points (a, 0) and (0, b), then `1/"a" + 1/"b"` =

Select the correct option from the given alternatives:

If A(1, −2), B(−2, 3) and C(2, −5) are the vertices of ∆ABC, then the equation of the median BE is

Select the correct option from the given alternatives:

The equation of the line through (1, 2), which makes equal intercepts on the axes, is

Select the correct option from the given alternatives:

If the line kx + 4y = 6 passes through the point of intersection of the two lines 2x + 3y = 4 and 3x + 4y = 5, then k =

Select the correct option from the given alternatives:

The equation of a line, having inclination 120° with positive direction of X−axis, which is at a distance of 3 units from the origin is

Select the correct option from the given alternatives:

A line passes through (2, 2) and is perpendicular to the line 3x + y = 3. Its y−interecpt is

Select the correct option from the given alternatives:

The angle between the line `sqrt(3)x - y - 2` = 0 and `x - sqrt(3)y + 1` = 0 is 

Select the correct option from the given alternatives:

If kx + 2y − 1 = 0 and 6x − 4y + 2 = 0 are identical lines, then determine k

Select the correct option from the given alternatives:

Distance between the two parallel lines y = 2x + 7 and y = 2x + 5 is

Answer the following question:

Find the value of k if the slope of the line passing through the points P(3, 4), Q(5, k) is 9

Answer the following question:

Find the value of k the points A(1, 3), B(4, 1), C(3, k) are collinear

Answer the following question:

Find the value of k the point P(1, k) lies on the line passing through the points A(2, 2) and B(3, 3)

Answer the following question:

Reduce the equation 6x + 3y + 8 = 0 into slope-intercept form. Hence find its slope

Answer the following question:

Find the distance of the origin from the line x = – 2

Answer the following question:

Does point A(2, 3) lie on the line 3x + 2y – 6 = 0? Give reason.

Answer the following question:

Which of the following lines passes through the origin?

Answer the following question:

Obtain the equation of the line which is parallel to the X−axis and 3 unit below it.

Answer the following question:

Obtain the equation of the line which is parallel to the Y−axis and 2 units to the left of it.

Answer the following question:

Obtain the equation of the line which is parallel to the X−axis and making an intercept of 5 on the Y−axis.

Answer the following question:

Obtain the equation of the line which is parallel to the Y−axis and making an intercept of 3 on the X−axis.

Answer the following question:

Obtain the equation of the line containing the point (2, 3) and parallel to the X-axis.

Answer the following question:

Obtain the equation of the line containing the point (2, 4) and perpendicular to the Y−axis

Answer the following question:

Find the equation of the line having slope 5 and containing point A(–1, 2).

Answer the following question:

Find the equation of the line containing the point T(7, 3) and having inclination 90°.

Answer the following question:

Find the equation of the line through the origin which bisects the portion of the line 3x + 2y = 2 intercepted between the co−ordinate axes.

Answer the following question:

Find the equation of the line passing through the points S(2, 1) and T(2, 3)

Answer the following question:

Find the distance of the origin from the line 12x + 5y + 78 = 0

Answer the following question:

Find the distance between the parallel lines 3x + 4y + 3 = 0 and 3x + 4y + 15 = 0

Answer the following question:

Find the equation of the line which contains the point A(3, 5) and makes equal intercepts on the co-ordinates axes.

Answer the following question:

The vertices of a triangle are A(1, 4), B(2, 3) and C(1, 6). Find equations of the sides.

Answer the following question:

The vertices of a triangle are A(1, 4), B(2, 3) and C(1, 6). Find equations of the medians.

Answer the following question:

The vertices of a triangle are A(1, 4), B(2, 3) and C(1, 6) Find equations of Perpendicular bisectors of sides

Answer the following question:

The vertices of a triangle are A(1, 4), B(2, 3) and C(1, 6) Find equations of altitudes of ∆ABC

Answer the following question:

Find the equation of the line which passes through the point of intersection of lines x + y − 3 = 0, 2x − y + 1 = 0 and which is parallel X-axis

Answer the following question:

Find the equation of the line which passes through the point of intersection of lines x + y + 9 = 0, 2x + 3y + 1 = 0 and which makes X-intercept 1.

Answer the following question:

Find the equation of the line through A(−2, 3) and perpendicular to the line through S(1, 2) and T(2, 5)

Answer the following question:

Find the X−intercept of the line whose slope is 3 and which makes intercept 4 on the Y−axis

Answer the following question:

Find the distance of P(−1, 1) from the line 12(x + 6) = 5(y − 2)

Answer the following question:

Line through A(h, 3) and B(4, 1) intersect the line 7x − 9y − 19 = 0 at right angle Find the value of h

Answer the following question:

Two lines passing through M(2, 3) intersect each other at an angle of 45°. If slope of one line is 2, find the equation of the other line.

Answer the following question:

Find the Y-intercept of the line whose slope is 4 and which has X intercept 5

Answer the following question:

Find the equations of the diagonals of the rectangle whose sides are contained in the lines x = 8, x = 10, y = 11 and y = 12

Answer the following question:

A(1, 4), B(2, 3) and C(1, 6) are vertices of ∆ABC. Find the equation of the altitude through B and hence find the co-ordinates of the point where this altitude cuts the side AC of ∆ABC.

Answer the following question:

The vertices of ∆PQR are P(2, 1), Q(−2, 3) and R(4, 5). Find the equation of the median through R.

Answer the following question:

A line perpendicular to segment joining A(1, 0) and B(2, 3) divides it internally in the ratio 1 : 2. Find the equation of the line.

Answer the following question:

Find the co-ordinates of the foot of the perpendicular drawn from the point P(−1, 3) the line 3x − 4y − 16 = 0

Answer the following question:

Find points on the X-axis whose distance from the line `x/3 + y/4` = 1 is 4 unit

Answer the following question:

The perpendicular from the origin to a line meets it at (−2, 9). Find the equation of the line.

Answer the following question:

P(a, b) is the mid point of a line segment between axes. Show that the equation of the line is `x/"a" + y/"b"` = 2

Answer the following question:

Find the distance of the line 4x − y = 0 from the point P(4, 1) measured along the line making an angle of 135° with the positive X-axis

Answer the following question:

Show that there are two lines which pass through A(3, 4) and the sum of whose intercepts is zero.

Answer the following question:

Show that there is only one line which passes through B(5, 5) and the sum of whose intercept is zero.