Question

Find the power of point (1,2) w.r.t the circle x^2+y^2+6x+8y-96=0

Answer 1

EXPLANATION.

$\sf : \implies \: points \: \: (1,2) \\ \\ \sf : \implies \: equation \: of \: circle \: = {x}^{2} + {y}^{2} + 6x + 8y - 96 = 0$

$\sf : \implies \: power \: point \: ( x_{1}, y_{1}) \: w.r.t \: circle \: \\ \\ \sf : \implies \: t \: = \sqrt{ s_{1} }$

$\sf : \implies \: \sqrt{(1) {}^{2} + {2}^{2} + 6(1) + 8(2) - 96 } = 0 \\ \\ \sf : \implies \: \sqrt{1 + 4 + 6 + 16 - 96} = 0 \\ \\ \sf : \implies \sqrt{27 - 96} = 0 \\ \\ \sf : \implies \: \sqrt{ - 69} = 0$