Mathematics - Circle Question with Solution | TestHub

MathematicsCircleRadical Axis & Radical Centre, Coaxial system of circles, Orthogonality of two circlesMedium2 minPYQ_2003

MathematicsMediumsingle choice

If the two circles $(x - 1)^{2} + (y - 3)^{2} = r^{2}$ and $x^{2} + y^{2} - 8 x + 2 y + 8 = 0$ intersect in two distinct point, then

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Solution:

$∣ r_{1} - r_{2} ∣ = C_{1} C_{2}$ for intersection $\Rightarrow r - 3 < 5 \Rightarrow r < 8$
and $r_{1} + r_{2} > C_{1} C_{2}, r + 3 > 5 \Rightarrow r = 2$
From (1) and (2), $2 < r < 8$ .

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

⏱ 2mℹ️ Source: PYQ_2003

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