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 $C_{3}$ at $R_{2}$ and $R_{3},$ respectively. Suppose $C_{2}$ and $C_{3}$ have equal radii $2 \sqrt{3}$ and centres $Q_{2}$ and $Q_{3},$ respectively. If $Q_{2}$ and $Q_{3}$ lie on the Y-axis, then

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away

An Intiative by Sri Chaitanya

$Q_{2} Q_{3} = 12$

$R_{2} R_{3} = 4 \sqrt{6}$

$area of the Δ O R_{2} R_{3} i s = 6 \sqrt{2}$

$area of the Δ P Q_{2} Q_{3} i s = 4 \sqrt{2}$

answer is B, A, C.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

Conceptual

Watch 3-min video & get full concept clarity

JEE

NEET

Foundation JEE

Foundation NEET

CBSE