Properties of...

Properties of Orthogonality of Two Circles

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Two circles $x^{2} + y^{2} + 2 g_{1} x + 2 f_{1} y + c_{1} = 0 a n d x^{2} + y^{2} + 2 g_{2} x + 2 f_{2} y + c^{2} = 0$ are said to be orthogonal. Then $2 g_{1} g_{2} + 2 f_{1} f_{2} = c_{1} + c_{2}$

True
False

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Q. A circle S passes through the point (0, 1) and is orthogonal to the circles

(x - 1)^{2} + y^{2} = 16

and

x^{2} + y^{2} = 1

then,

Radius of S is 8
Radius of S is 7
Centre of S is (-7, 1)
Center of S is (-8, 1)

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