The locus of centre of a circle passing throu | vedclass

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Question

(a) Let equation of circle be ${x^2} + {y^2} + 2gx + 2fy + c = 0$ with ${x^2} + {y^2} = {p^2}$ cutting orthogonally,

we get $0 + 0 = + c - {p^2}$

Vedclass · Accepted Answer

$2ax + 2by - ({a^2} + {b^2} + {p^2}) = 0$

Vedclass · Answer

(a) Let equation of circle be ${x^2} + {y^2} + 2gx + 2fy + c = 0$ with ${x^2} + {y^2} = {p^2}$ cutting orthogonally,

we get $0 + 0 = + c - {p^2}$

or $c = {p^2}$ and passes through $(a, b)$,

we get ${a^2} + {b^2} + 2ga + 2fb + {p^2} = 0$ or

$2ax + 2by - ({a^2} + {b^2} + {p^2}) = 0$

Required locus as centre $( - g,\; - f)$ is changed to $(x, y)$.

The locus of centre of a circle passing through $(a, b)$ and cuts orthogonally to circle ${x^2} + {y^2} = {p^2}$, is

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