Mathematics - Circle Question with Solution | TestHub

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

MathematicsMediummultiple choice

Two circles $x^{2} + y^{2} + p x + p y - 7 = 0$ and $x^{2} + y^{2} - 10 x + 2 p y + 1 = 0$ will cut orthogonally if the value of $p$ is

Answer:

C, D

Solution:

The given circles will cut orthogonally if $2 (\frac{p}{2}) (\frac{- 10}{2}) + 2 (\frac{p}{2}) (\frac{2 p}{2}) = - 7 + 1$

or $p^{2} - 5 p + 6 = 0$ of if $p = 2$ or 3 .

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

⏱ 2mℹ️ Source: QB

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