ParabolaHard
Question
The straight line joining any point P on the parabola y2 = 4ax to the vertex and perpendicular from the focus to the tangent at P, intersect at R, then the equation of the locus of R is -
Options
A.x2 + 2y2 - ax = 0
B.2x2 + y2 - 2ax = 0
C.2x2 + 2y2 - ay = 0
D.2x2 + y2 - 2ay = 0
Solution
Let point P(at2, 2at) on y2 = 4ax
equation of line joining P & vertex
y =
x ... (1)
equation of line which is
perpendicular tangent at P & passing S(a, 0) is
y + tx = at ....(2)
from (1) & (2) eliminating t
we get the locus of R
y2 + 2x2 = 2ax
equation of line joining P & vertex
y =
x ... (1)equation of line which is
perpendicular tangent at P & passing S(a, 0) is
y + tx = at ....(2)
from (1) & (2) eliminating t
we get the locus of R
y2 + 2x2 = 2ax
Create a free account to view solution
View Solution FreeMore Parabola Questions
If two tangents drawn from a point P to the parabola y2 = 4x are at right angles, then the locus of P is...Length of the normal chord of the parabola, y2 = 4x, which makes an angle of with the axis of x is -...The equation of the common tangent to the curves y2 = 8x and yx = - 1 is...If the tangents and normals at the extremities of a focal chord of a parabola intersect at (x1, y1) and (x2, y2) respect...If (t2, 2t) is one end of a focal chord of the parabola y2 = 4x then the length of the focal chord will be -...