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
The area of the region bounded by the parabola (y - 2)2 = x - 1, the tangent to the parabola at the point (2, 3) and the...The tangent PT and the normal PN to the parabola y2 = 4ax at a point P on it meet its axis at points T and N, respective...The equation of image of parabola x2 = 4y with respect to line mirror x - y + 2 = 0 is -...The line 4x - 7y + 10 = 0 intersects the parabola, y2 = 4x at the points A & B. The co-ordinates of the point of interse...Let (x, y) be any point on the parabola y2 = 4x. Let P be the point that divides the line segment from (0, 0) to (x, y) ...