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Mathematics - Circle Question with Solution | TestHub

MathematicsCirclePosition of a point w.r.t a circle, Parametric equation of a circleMedium2 minQB

MathematicsMediumsingle choice

$(1, 4)$ lies inside $x^{2} + y^{2} - 6 x - 10 y + p = 0$ , which does not touch or meet either coordinate axis. Find the range of $p$ .

Options:

Answer:

Solution:

The centre is $(3, 5)$ and radius squared $34 - p$ . To contain $(1, 4)$ strictly requires $34 - p > 5$ , hence $p < 29$ . Not meeting either axis requires radius < 3, hence $34 - p < 9$ and $p > 25$ .

Stream:JEESubject:MathematicsTopic:CircleSubtopic:Position of a point w.r.t a circle, Parametric equation of a circle

⏱ 2mℹ️ Source: QB

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