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Mathematics - Circle Question with Solution | TestHub

MathematicsCircleTangent & NormalMedium2 minQB

MathematicsMediumsingle choice

A circle passes through $(2, 2)$ and $(9, 9)$ and touches the $x$ -axis. The $x$ -coordinate of contact is

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Answer:

Solution:

The family is $(x - 2) (x - 9) + (y - 2) (y - 9) + t (y - x) = 0$ . On $y = 0$ , this becomes $x^{2} - (11 + t) x + 36 = 0$ . Tangency means its repeated root has square 36, hence contact $x = \pm 6$ .

Stream:JEESubject:MathematicsTopic:CircleSubtopic:Tangent & Normal

⏱ 2mℹ️ Source: QB

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