If a circle passes through the point (1, 2) a | vedclass

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Question

(c) Let equation of circle be ${x^2} + {y^2} + 2gx + 2fy + c = 0$

It passes through $(1, 2)$

$i.e.$ $1 + 4 + 2g + 4f + c = 0$ and is orthogonal

Vedclass · Accepted Answer

$2x + 4y - 9 = 0$

Vedclass · Answer

(c) Let equation of circle be ${x^2} + {y^2} + 2gx + 2fy + c = 0$

It passes through $(1, 2)$

$i.e.$ $1 + 4 + 2g + 4f + c = 0$ and is orthogonal w.r.t ${x^2} + {y^2} = 4$.

Therefore, $2g 	imes 0 + 2f 	imes 0 = - c + 4$ or $c = 4$

Hence, we get $2g + 4f + 9 = 0$,

then $2x + 4y - 9 = 0$ is the required locus.

If a circle passes through the point $(1, 2)$ and cuts the circle ${x^2} + {y^2} = 4$ orthogonally, then the equation of the locus of its centre is

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