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Parabola question

2016 · Shift 2 · Q31

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PYQ Library
JEE Advanced
Mathematics
Parabola
2016 · Shift 2 · Q31

Parabola question

2016 · Shift 2 · Q31

JEE AdvancedMathematicsParabolaMultiple correct+4 / −2

Let

P

be the point on the parabola

{y^2} = 4x

which is at the shortest distance from the center

S

of the circle

{x^2} + {y^2} - 4x - 16y + 64 = 0

. Let

Q

be the point on the circle dividing the line segment

SP

internally. Then

A
$SP = 2\sqrt 5$
B
$SQ:QP = \left( {\sqrt 5 + 1} \right):2$
C
the $x$ -intercept of the normal to the parabola at $P$ is $6$
D
the slope of the tangent to the circle at $Q$ is ${1 \over 2}$

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