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Properties of Orthogonality of Two Circles

Two given cir...

Question

Two given circles $x^{2} + y^{2} + a x + b y + c = 0$ and $x^{2} + y^{2} + d x + e y + f = 0$ will intersect each other orthogonally, only when

A

a+b+c = d+e+f

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B

ad+be = c+f

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C

2ad+2be = c+f

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Solution

From Condition for orthogonal intersection,
$\frac{a d}{2} + \frac{b e}{2} = c + f$ .

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Q. Two given circles

x^{2} + y^{2} + a x + b y + c = 0

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will intersect each other orthogonally, only when

Q. Two given circles

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x^{2} + y^{2} + 8 x - 6 y - 7 = 0

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Properties of Orthogonality of Two Circles

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