Mathematics - Circle Question with Solution | TestHub

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

MathematicsMediumsingle choice

Find the minimum radius of a circle orthogonal to both $x^{2} + y^{2} - 12 x + 35 = 0$ and $x^{2} + y^{2} + 4 x + 3 = 0$ .

Options:

Answer:

Solution:

The variable centre is on their radical axis $x = 2$ . The orthogonal radius squared equals its power relative to either given circle, minimised at $(2, 0)$ , giving $r^{2} = 4 - 24 + 35 = 15$ .

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

⏱ 2mℹ️ Source: QB

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