The circles x 2- y 2- kx -4 y -20 and x 2- y 2-6 x -8 y -10-0 intersect orthogonally- Also circles x 2- y 2- p x - y -1-0kand p x 2- y 2- x - y -1 intersect orthogonally- Then n - p equals1A- 1B- 2-2C- 2D- 4

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Obtaining Centre and Radius of a Circle from General Equation of a Circle

The circles x...

Question

The circles $x^{2} + y^{2} + k x + 4 y = 20$ and $x^{2} + y^{2} + 6 x - 8 y + 10 = 0$ intersect orthogonally. Also circles $x^{2} + y^{2} - p (x - y) + 1 = 0$ and $p (x^{2} + y^{2}) + x - y = 1$ intersect orthogonally. Then $\frac{k}{p}$ equals

\frac{1}{4}

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\frac{1}{2}

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2

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4

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