Balbharati solutions for Mathematics and Statistics 1 (Commerce) [English] 11 Standard Maharashtra State Board chapter 5 - Locus and 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 points 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 co-ordinates of the points 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 co-ordinates of the points 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 co-ordinates of the points D(3, 3)

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

Obtain the new equations 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 equations 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 equations 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

Find the slope of the following lines which pass through the point: (2, – 1), (4, 3)

Find the slope of the following lines which pass through the point: (– 2, 3), (5, 7)

Find the slope of the following lines which pass through the point: (2, 3), (2, – 1)

Find the slope of the following lines which pass through the point: (7, 1), (– 3, 1)

If the X and Y-intercepts of line 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 45°.

A line makes intercepts 3 and 3 on coordinate 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 clockwise.

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

Write the equation of the line: parallel to the X-axis and at a distance of 5 units from it and above it.

Write the equation of the line: parallel to the Y-axis and at a distance of 5 units from it and to the left of it.

Write the equation of the line: parallel to the X-axis and at a distance of 4 units from the point (−2, 3).

Obtain the equation of the line: parallel to the X-axis and making an intercept of 3 units on the Y-axis.

Obtain the equation of the line: parallel to the Y-axis and making an intercept of 4 units 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).

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

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

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

The vertices of a triangle are A(3, 4), B(2, 0) and C(1, 6). Find the equations of the line passing through the mid points of sides AB and BC.

Find the x and y-intercepts of the following line: `x/3 + y/2` = 1

Find the x and y-intercepts of the following line: `(3x)/2 + (2y)/3` = 1

Find the x and y-intercepts of the following line: 2x – 3y + 12 = 0

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

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

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 : 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`

Show that the lines x – 2y – 7 = 0 and 2x − 4y + 5 = 0 are parallel to each other.

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

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

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 point A(– 2, 3) from the line 12x – 5y – 13 = 0.

Find the distance between parallel lines 9x + 6y − 7 = 0 and 9x + 6y − 32 = 0.

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.

D(– 1, 8), E(4, – 2), F(– 5, – 3) are midpoints of sides BC, CA and AB of ΔABC Find: equations of sides of ΔABC.

D(– 1, 8), E(4, – 2), F(– 5, – 3) are midpoints of sides BC, CA and AB of ΔABC Find: co-ordinates of the circumcentre of ΔABC.

Find the slope of the line passing through the following point: (1, 2), (3, – 5)

Find the slope of the line passing through the following point: (1, 3), (5, 2)

Find the slope of the line passing through the following point: (–1, 3), (3, –1)

Find the slope of the line passing through the following point: (2, – 5), (3, – 1)

Find the slope of the line which makes an angle of 120° with the positive X-axis.

Find the slope of the line which makes intercepts 3 and – 4 on the axes.

Find the slope of the line which passes through the points A(–2, 1) and the origin.

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

Find the value of k: the points (1, 3), (4, 1), (3, k) are collinear.

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).

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

Verify that A(2, 7) is not a point on the line x + 2y + 2 = 0.

Find the X-intercept of the line x + 2y – 1 = 0

Find the slope of the line y – x + 3 = 0.

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

Which of the following lines passes through the origin?

Obtain the equation of the line which is: parallel to the X-axis and 3 units below it.

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

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

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

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

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

Obtain the equation of the line containing the point: (2, 5) and perpendicular to the X−axis.

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

Find the equation of the line: containing the point (2, 1) and having slope 13.

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

Find the equation of the line: containing the origin and having inclination 90°.

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.

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

Find the equation of the line: having slope 5 and making intercept 5 on the X−axis.

Find the equation of the line: having an inclination 60° and making intercept 4 on the Y-axis.

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

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

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

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