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Parabola question

2014 · Shift 2 · Q26

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PYQ Library
JEE Advanced
Mathematics
Parabola
2014 · Shift 2 · Q26

Parabola question

2014 · Shift 2 · Q26

JEE AdvancedMathematicsParabolaMCQ+3 / −1

Let

a, r, s, t

be nonzero real numbers. Let

P\,\,\left( {a{t^2},2at} \right),\,\,Q,\,\,\,R\,\,\left( {a{r^2},2ar} \right)

and

S\,\,\left( {a{s^2},2as} \right)

be distinct points on the parabola

{y^2} = 4ax

. Suppose that

PQ

is the focal chord and lines

QR

and

PK

are parallel, where

K

is the point

(2a,0)

If

st=1

, then the tangent at

P

and the normal at

S

to the parabola meet at a point whose ordinate is

A
${{{{\left( {{t^2} + 1} \right)}^2}} \over {2{t^3}}}$
B
${{a{{\left( {{t^2} + 1} \right)}^2}} \over {2{t^3}}}$
C
${{a{{\left( {{t^2} + 1} \right)}^2}} \over {{t^3}}}$
D
${{a{{\left( {{t^2} + 2} \right)}^2}} \over {{t^3}}}$

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