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 $(h, k), 4\left(h^2+k^2\right)$ is equal to __________.
Answer (integer)
9
Solution
<p>Circle will touch internally</p>
<p>$$\begin{aligned}
& C_1 C_2=\left|r_1-r_2\right| \\
& =\sqrt{h^2+k^2}=3-\sqrt{h^2+k^2} \\
& \Rightarrow 2 \sqrt{h^2+k^2}=3 \\
& \Rightarrow h^2+k^2=\frac{9}{4} \\
& \therefore 4\left(h^2+k^2\right)=9
\end{aligned}$$</p>
About this question
Subject: Mathematics · Chapter: Circles · Topic: Equation of a Circle
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