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Mathematics - Circle Question with Solution | TestHub

MathematicsCircleRadical Axis & Radical Centre, Coaxial system of circles, Orthogonality of two circlesMedium2 minPYQ_2004

MathematicsMediumsingle choice

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

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Solution:

Let the circle be $x^{2} + y^{2} + 2 gx + 2 f y + c = 0 \Rightarrow c = 4$ and it passes through $(a, b)$ $\Rightarrow a^{2} + b^{2} + 2 ga + 2 fb + 4 = 0$ Hence locus of the centre is $2 a x + 2 b y - (a^{2} + b^{2} + 4) = 0$

Stream:JEESubject:MathematicsTopic:CircleSubtopic:Radical Axis & Radical Centre, Coaxial system of circles, Orthogonality of two circles

⏱ 2mℹ️ Source: PYQ_2004

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