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  • The tangent and normal at a point  to the parabola&nbs

The tangent and normal at a point \mathrm{P \equiv(16,16)} to the parabola \mathrm{y^2=16 x} intersect the x-axis at A and B respectively. Circle \mathrm{C_1} is drawn through \mathrm{P, A} and B. Another circle \mathrm{C_2 x^2+y^2+4 x +2 y+10=0} cuts the parabola orthogonally and passes through P. Find the equation of the common chord of \mathrm{\mathrm{C}_1} and \mathrm{\mathrm{C}_2.}

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best_answer

C_1: x^2+y^2-8 x-384=0

2 x^2+y^2+4 x+2 y+10=0

C_2-C_1=\left(2 x^2+y^2+4 x+2 y+10\right)-\left(x^2+y^2-8 x-384\right)

x^2+12 x+2 y+394=0

Posted by

Divya Sharma

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