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The circle {C}_{{1}}:{x}^{{2}}+{y}^{{2}}={3}, with centre at O

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The circle $C_{1} : x^{2} + y^{2} = 3,$ with centre at O, intersects the parabola $x^{2} = 2 y$ at the point P in the first quadrant. Let the tangent to the circle $C_{1}$ at P touches other two circles $C_{2} and C_{3} a t R_{2} and R_{3},$ respectively. Suppose $C_{2} and C_{3}$ have equal radii $23$ and centres at $Q_{2}$ and $Q_{3}$ respectively. If $Q_{2}$ and $Q_{3}$ lie on the y-axis, then (a) $Q 2 Q 3 = 12$ (b) $R 2 R 3 = 46$ (c)area of triangle $O R 2 R 3$ is $62$ (d)area of triangle $P Q 2 Q 3 i s = 42$

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Charlotte Discussed

The circle

C_{1} : x^{2} + y^{2} = 3,

with centre at O, intersects the parabola

x^{2} = 2 y

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} a t R_{2} and R_{3},

respectively. Suppose

C_{2} and C_{3}

have equal radii

23

and centres at

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 = 46

(c)area of triangle

O R 2 R 3

62

(d)area of triangle

P Q 2 Q 3 i s = 42

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Question Text	The circle $C_{1} : x^{2} + y^{2} = 3,$ with centre at O, intersects the parabola $x^{2} = 2 y$ at the point P in the first quadrant. Let the tangent to the circle $C_{1}$ at P touches other two circles $C_{2} and C_{3} a t R_{2} and R_{3},$ respectively. Suppose $C_{2} and C_{3}$ have equal radii $23$ and centres at $Q_{2}$ and $Q_{3}$ respectively. If $Q_{2}$ and $Q_{3}$ lie on the y-axis, then (a) $Q 2 Q 3 = 12$ (b) $R 2 R 3 = 46$ (c)area of triangle $O R 2 R 3$ is $62$ (d)area of triangle $P Q 2 Q 3 i s = 42$
Answer Type	Video solution: 1
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