AP EAMCET · Maths · Circle
If power of a point \((4,2)\) with respect to the circle \(x^2+y^2\) \(-2 \alpha x+6 y+\alpha^2-16=0\) is 9 , then the sum of the lengths of all possible intercepts made by such circles on the coordinate axes is
- A \(16+4 \sqrt{6}\)
- B \(16+4 \sqrt{6}-6 \sqrt{2}\)
- C \(16+4 \sqrt{6}+6 \sqrt{2}\)
- D \(16+6 \sqrt{2}\)
Answer & Solution
Correct Answer
(A) \(16+4 \sqrt{6}\)
Step-by-step Solution
Detailed explanation
\(x^2+y^2-2 \alpha x+6 y+\alpha^2-16=0\) Centre \((C)=(\alpha,-3) ;(x-\alpha)^2+(y+3)^2=25\) Radius \((R)=5\) \(d=\) distance between centre and \((4,2)\) \(\Rightarrow d^2=(\alpha-4)^2+25\) Power \(=d^2-R^2 \Rightarrow 9=(\alpha-4)^2 \mathrm{~m} \Rightarrow \alpha=1,7\) When…
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