QJEEM24Ma05ba: JEE Main 2024 Mathematics - Class 11 JEEM24Ma05ba Solution: Let the centre of a circle, passing through the points ( 0 , 0…

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QJEEM24Ma05ba: JEE Main 2024 Mathematics - Class 11 JEEM24Ma05ba Solution: Let the centre of a circle, passing through the points ( 0 , 0…

Let the centre of a circle, passing through the points $(0, 0), (1, 0)$ and touching the circle $x^{2} + y^{2} = 9$ , be $(h, k)$ . Then for all possible values of the coordinates of the centre $(h, k), 4 (h^{2} + k^{2})$ is equal to __________.

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Accepted Answer

Circle will touch internally

$\begin{aligned} C_{1} C_{2} = | r_{1} - r_{2} | \\ = \sqrt{h^{2} + k^{2}} = 3 - \sqrt{h^{2} + k^{2}} \\ \Rightarrow 2 \sqrt{h^{2} + k^{2}} = 3 \\ \Rightarrow h^{2} + k^{2} = \frac{9}{4} \\ ∴ 4 (h^{2} + k^{2}) = 9 \end{aligned}$

QJEEM24Ma05ba: JEE Main 2024 Mathematics - Class 11 JEEM24Ma05ba Solution: Let the centre of a circle, passing through the points ( 0 , 0…

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