Mathematics - Circle Question with Solution | TestHub

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

MathematicsMediumsingle choice

All circles orthogonal to both $x^{2} + y^{2} + 6 x + 5 = 0$ and $x^{2} + y^{2} - 6 y + 5 = 0$ pass through which fixed points?

Options:

Answer:

Solution:

Their centres lie on $x + y = 0$ ; put the centre at $(t, - t)$ . Orthogonality fixes the radius and gives the family $x^{2} + y^{2} - 5 - 2 t (x - y + 3) = 0$ . Its fixed points solve $x^{2} + y^{2} = 5, x - y + 3 = 0$ , giving $(- 1, 1), (- 2, 2)$ .

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

⏱ 2mℹ️ Source: QB

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