Equation of circle touching the line at (1, 3) and intersecting the circle orthogonally, is gksxk tks o`Ùk dks yfEcd izfrPNsn djrk

JEE MainMathematicsEasyCircles

Equation of circle touching the line $x + y = 4$ at (1, 3) and
intersecting the circle $x^{2} + y^{2} = 4$ orthogonally, is
gksxk tks o`Ùk $x^{2} + y^{2} = 4$ dks yfEcd izfrPNsn djrk

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Circle

\Rightarrow x^{2} + y^{2} + x(\lambda + 2) + y(\lambda - 6) + (10 - 4\lambda) = 0

2g_{1}g_{2} + 2f_{1}f_{2} = 4 + \lambda_{2}

\Rightarrow 0 + 0 = 10 - 4\lambda - 4 \Rightarrow \lambda = \frac{3}{2}

\Rightarrow x^{2} + y^{2} - \frac{x}{2} - \frac{9y}{2} + 4 = 0

Source: Grass-G / M-27 Mathematics Paper 2 15 Jan.docx

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