A variable tangent to the parabola ${y^2} = 4ax$ meets the parabola ${y^2} = - 4ax$ at $P$ and $Q$. The locus of the mid-point of $PQ$ is

JEE MATHEMATICS MCQ: PARABOLA

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Analyzing +4 | -1

A variable tangent to the parabola

{y^2} = 4ax

meets the parabola

{y^2} = - 4ax

P

and

Q

. The locus of the mid-point of

PQ

View answer and explanation

Correct option: C

{y^2} - \frac{4}{3}ax

Option C is correct because the locus of the midpoint is found by using the tangent equation and properties of the parabola.

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y=x^2

y=-(x-2)^2

P

y^2=16 x

P

P,Q,R

{y^2} = 4x

P

R

Q

PR

(1,0)

y^2+4 x=8

x^2=-16 y

I

{y^2} = 4ax

SP

SQ

PQ,S

SP,l

SQ