WBJEE · Maths · Circle
If two circles which pass through the points (0, a) and (0, - a) and touch the line y = mx + c, cut orthogonally then
- A \(c^2=a^2\left(1+m^2\right)\)
- B \(c^2=a^2\left(2+m^2\right)\)
- C \(c^2=a^2\left(1+2 m^2\right)\)
- D \(2 c^2=a^2\left(1+m^2\right)\)
Answer & Solution
Correct Answer
(B) \(c^2=a^2\left(2+m^2\right)\)
Step-by-step Solution
Detailed explanation
Let the equation of the circles be \(x^2+y^2+2 g x+2 f y+d=0 \quad \ldots(1)\) Since, these circles pass through \((0, a)\) and \((0,-a)\) then \(a^2+2 f a+d=0 \quad \ldots(2)\)and \(a^2-2 f a+d=0 \quad \ldots(3)\) Solving (2) and (3), we get…
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