JEE Mains · Maths · STD 11 - 10.1 circle and system of circle
Let the centre of a circle, passing through the point \((0,0),(1,0)\) 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 .............
- A \(1\)
- B \(2\)
- C \(6\)
- D \(9\)
Answer & Solution
Correct Answer
(D) \(9\)
Step-by-step Solution
Detailed explanation
\( (\mathrm{x}-\mathrm{h})^2+(\mathrm{y}-\mathrm{k})^2=\mathrm{h}^2+\mathrm{k}^2 \) \( \mathrm{x}^2+\mathrm{y}^2-2 \mathrm{hx}-2 \mathrm{ky}=0 \) \( \because \text { passes through }(1,0) \) \( \Rightarrow 1+0-2 \mathrm{~h}=0 \) \( \Rightarrow \mathrm{h}=1 / 2 \)…
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