The tangents to the parabola $y^2=4 a x$ at $P\left(a t_1^2, 2 a t_1\right)$ and $Q\left(a t_2^2, 2 a t_2\right)$ intersect on its axis, then

JEE MATHEMATICS MCQ: PARABOLA

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The tangents to the parabola

y^2=4 a x

P\left(a t_1^2, 2 a t_1\right)

and

Q\left(a t_2^2, 2 a t_2\right)

intersect on its axis, then

View answer and explanation

Correct option: B

t_1=-t_2

Option B (

t_1=-t_2

) is correct because the point of intersection of the tangents lies on the x-axis, implying that the y-coordinate of the intersection point is zero.

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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