Question

Find an equation of the tangent line to the circle x^2 +y^2=24 at the point (-2 square root 5, 2).

Answer 1

$Circle:\\(x-a)^2+(y-b)^2=r^2\\\\Point:\\P(x_P;\ y_P)\\\\tangent\ line\ to\ the\ circle:\\\\k:(x_p-a)(x-a)+(y_p-b)(y-b)=r^2$


$Circle:\\x^2+y^2=24\\\\center\ of\ circle:S(0;\ 0)\\\\radius:r=\sqrt{24}\\\\Point:P(-2\sqrt5;\ 2)$

$tangent\ line\ to\ the\ circle:\\\\k:(-2\sqrt5-0)(x-0)+(2-0)(y-0)=(\sqrt{24})^2\\\\-2\sqrt5x+2y=24\\\\2y=2\sqrt5x+24\ \ \ \ /:2\\\\y=\sqrt5x+12-answer$