If two parabolas y^2=4ax–k and x^2=4ay–k have only one common point P, then the equation of normal to y^2=4ax–k at P is

Question

MARKS Content Team · Accepted Answer

Correct answer: (A) y+x=4a. Parabolas y^2=4ax–k and x^2=4ay–k touche each other at line y=x (∵ both parabola are inverse of each other) ⇒ y=x is a common tangent at P ⇒ we get point P by solving y^2=4ax–k and y=x ⇒ point of contact P is 2a,2a ⇒ equation of normal at P2a,2a is x+y=4a

If two parabolas $y^{2} = 4 a (x - k)$ and $x^{2} = 4 a (y - k)$ have only one common point $P$ , then the equation of normal to $y^{2} = 4 a (x - k)$ at $P$ is

Solution

More Parabola Questions

If two parabolas y2=4ax–k and x2=4ay–k have only one common point P, then the equation of normal to y2=4ax–k at P is

Solution

More Parabola Questions

If two parabolas $y^{2} = 4 a (x - k)$ and $x^{2} = 4 a (y - k)$ have only one common point $P$ , then the equation of normal to $y^{2} = 4 a (x - k)$ at $P$ is