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JEE Advanced 2015Paper 1

Exam: JEE Advanced
Year: 2015
Paper: Paper 1
Subject: Mathematics
Chapter: Parabola

JEE Advanced 2015 · Paper 1 · Mathematics · Parabola

If the normal of the parabola y ^ 2 = 4x drawn at the end points of...

If the normal of the parabola

{y}^{2} = 4x

drawn at the end points of its latus rectum are tangents to the circle

{\left(x - 3\right)}^{2} + {\left(y + 2\right)}^{2} = {r}^{2},

then the value of

{r}^{2}

is

Correct answer

0

Step-by-step solution

End points of latus rectum

A ( 1, 2 ) , B ( 1, – 2 )

Equation of normal at

A

\left[\dfrac{dy}{dx} = 1\right]

<br >

y - 2 = - 1

\left(x - 1\right)

x + y - 3 = 0

...(i)

r =

Distance of line (i) from

\left(3, - 2\right)

r = \left|\dfrac{3 - 2 - 3}{\sqrt{2}}\right| = \sqrt{2}

{r}^{2} = 2

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