QJEEM24Ma5e35: JEE Main 2024 Mathematics - Class 11 JEEM24Ma5e35 Solution: Consider two circles C 1 : x 2 + y 2 = 25 and C 2 : ( x − α ) 2 …

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QJEEM24Ma5e35: JEE Main 2024 Mathematics - Class 11 JEEM24Ma5e35 Solution: Consider two circles C 1 : x 2 + y 2 = 25 and C 2 : ( x − α ) 2 …

Consider two circles $C_{1} : x^{2} + y^{2} = 25$ and $C_{2} : (x - α)^{2} + y^{2} = 16$ , where $α \in (5, 9)$ . Let the angle between the two radii (one to each circle) drawn from one of the intersection points of $C_{1}$ and $C_{2}$ be $\sin^{- 1} (\frac{\sqrt{63}}{8})$ . If the length of common chord of $C_{1}$ and $C_{2}$ is $β$ , then the value of $(α β)^{2}$ equals _______.

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Accepted Answer

$\begin{matrix} C_{1} : x^{2} + y^{2} = 25, C_{2} : (x - α)^{2} + y^{2} = 16 \\ 5 < α < 9 \end{matrix}$

JEE Main 2024 (Online) 30th January Evening Shift Mathematics - Circle Question 19 English Explanation

$\begin{aligned} θ = \sin^{- 1} (\frac{\sqrt{63}}{8}) \\ \sin θ = \frac{\sqrt{63}}{8} \end{aligned}$

Area of $△ OAP = \frac{1}{2} \times α (\frac{β}{2}) = \frac{1}{2} \times 5 \times 4 \sin θ$

$\begin{aligned} \Rightarrow & α β = 40 \times \frac{\sqrt{63}}{8} \\ α β = 5 \times \sqrt{63} \\ (α β)^{2} = 25 \times 63 = 1575 \end{aligned}$

QJEEM24Ma5e35: JEE Main 2024 Mathematics - Class 11 JEEM24Ma5e35 Solution: Consider two circles C 1 : x 2 + y 2 = 25 and C 2 : ( x − α ) 2 …

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