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Parabola question

2016 · Shift 1 · Q27

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PYQ Library
JEE Advanced
Mathematics
Parabola
2016 · Shift 1 · Q27

Parabola question

2016 · Shift 1 · Q27

JEE AdvancedMathematicsParabolaMultiple correct+4 / −2

The circle

{C_1}:{x^2} + {y^2} = 3,

with centre at

O

, intersects the parabola

{x^2} = 2y

at the point

P

in the first quadrant, Let the tangent to the circle

{C_1}

, at

P

touches other two circles

{C_2}

and

{C_3}

at

{R_2}

and

{R_3}

, respectively. Suppose

{C_2}

and

{C_3}

have equal radil

{2\sqrt 3 }

and centres

{Q_2}

and

{Q_3}

, respectively. If

{Q_2}

and

{Q_3}

lie on the

y

-axis, then

A
${Q_2}{Q_3} = 12$
B
${R_2}{R_3} = 4\sqrt 6$
C
area of the triangle $O{R_2}{R_3}$ is $6\sqrt 2$
D
area of the triangle $P{Q_2}{Q_3}$ is $4\sqrt 2$

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