AP EAMCET · Maths · Circle
The locus of centres of all circles which touch the line \(x=2 a\) and cut the circle \(x^2+y^2=a^2\) orthogonally is
- A \(y^2+4 a x-5 a^2=0\)
- B \(y^2+4 a x+5 a^2=0\)
- C \(y^2=4 a x-5 a^2\)
- D \(y^2=4 a x+5 a^2\)
Answer & Solution
Correct Answer
(A) \(y^2+4 a x-5 a^2=0\)
Step-by-step Solution
Detailed explanation
Let the center of the circle be \((h, k)\) and its radius be \(r\). Condition for touching the line \(x=2a\): \(r = |h-2a|\) \(r^2 = (h-2a)^2\) Condition for orthogonal intersection with \(x^2+y^2=a^2\): \(2(-h)(0) + 2(-k)(0) = (h^2+k^2-r^2) + (-a^2)\) \(0 = h^2+k^2-r^2-a^2\)…
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