Advertisements
Advertisements
प्रश्न
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.
उत्तर
Let P(x, y) be the point which divides AB internally in the ratio 1 : 2, where A(1, 0) and B(2, 3).
∴ x = `(1(2) + 2(1))/(1 + 2) = (2 + 2)/3 = 4/3`
and y = `(1(3) + 2(0))/(1 + 2) = (3 + 0)/3` = 1
∴ P ≡ `(4/3, 1)`
Now, slope of AB = `(3 - 0)/(2 - 1)` = 3
∴ slope of the line perpendicular to AB is `-1/3` and it is passing through `"P"(4/3, 1)`.
∴ equation of the required line is
y – 1 =`-1/3(x - 4/3)`
∴ 3y – 3 = `- x + 4/3`
∴ x + 3y = `13/3`
∴ 3x + 9y = 13
APPEARS IN
संबंधित प्रश्न
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 containing the origin and having inclination 60°
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°
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 the median AD
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:
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 the equations of perpendicular bisectors of sides of the triangle whose vertices are P(−1, 8), Q(4, −2), and R(−5, −3)
N(3, −4) is the foot of the perpendicular drawn from the origin to line L. Find the equation of line L.
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 the line kx + 4y = 6 passes through the point of intersection of the two lines 2x + 3y = 4 and 3x + 4y = 5, then k =
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:
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 passing through the points S(2, 1) and T(2, 3)
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:
Find the Y-intercept of the line whose slope is 4 and which has X intercept 5
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:
Show that there is only one line which passes through B(5, 5) and the sum of whose intercept is zero.
If the equation kxy + 5x + 3y + 2 = 0 represents a pair of lines, then k = ____________.
The lines `(x + 1)/(-10) = (y + 3)/-1 = (z - 4)/1` and `(x + 10)/(-1) = (y + 1)/-3 = (z - 1)/4` intersect at the point ______
The slope of normal to the curve x = `sqrt"t"` and y = `"t" - 1/sqrt"t"`at t = 4 is _____.
The angle between the lines x sin 60° + y cos 60° = 5 and x sin 30° + y cos 30° = 7 is ______
Suppose the line `(x - 2)/α = ("y" - 2)/(-5) = ("z" + 2)/2` lies on the plane x + 3y – 2z + β = 0. Then (α + β) is equal to ______.
Area of the parallelogram formed by the lines y = mx, y = mx + 1, y = nx and y = nx + 1 is equal to ______.
N(3, – 4) is the foot of the perpendicular drawn from the origin to a line L. Then, the equation of the line L is ______.
