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Mathematics - Circle Question with Solution | TestHub

MathematicsCircleFamily of circlesMedium2 minQB

MathematicsMediumsingle choice

A variable circle passes through $(0, 0)$ and touches $y = x$ . Its common chord with $x^{2} + y^{2} + 6 x + 8 y - 7 = 0$ always passes through

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Answer:

Solution:

The variable circle has equation $x^{2} + y^{2} + t (x - y) = 0$ . Subtracting gives the common-chord line $(6 - t) x + (8 + t) y - 7 =$ 0, containing (1/2, 1/2) for every $t$ .

Stream:JEESubject:MathematicsTopic:CircleSubtopic:Family of circles

⏱ 2mℹ️ Source: QB

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