If two parabolas y^2=4ax-k and x^2=4ay-k have only one common point P, then the coordinates of P are

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MARKS Content Team · Accepted Answer

Correct answer: (A) 2k,2k. Parabolas y^2=4ax-k and x^2=4ay-k touch each other at the line y=x (∵ both parabolas are inverse of each other) ⇒y=x is the common tangent at P ⇒ we get point P by solving y^2=4ax-k and y=x ⇒ point of contact P=2a,2a ⇒2a^2=4a2a-k⇒k=a⇒P=2k,2k

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

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More Parabola Questions

If two parabolas y2=4ax-k and x2=4ay-k have only one common point P, then the coordinates of P are

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 coordinates of $P$ are