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
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