Question

Find the equation of the tangent line at the given point on the following curve.

x^2+y^2=41, (-5,4)

Answer 1

$2x+2yy'=0$ hence $y'=-\frac{2x}{2y}=-\frac{x}{y}$ then $y'=5/4$ if $(-5,4)$ , hence equation of the tangent is $y-4=\frac{5}{4}(x+5)$ or $5x-4y+41=0$