Find the equation of the tangent line to a given curve at a given point

Question

Find the equation of the tangent line to the curve $x^2 - y^2 +2x-6=0$ in the point $(x,3)$, where $x<0.$ So I tried to find the derivative of the given curve, $2x-2yy' +2=0$...here I replaced the given coordinates and I have that $y'=-3/2$ I replace in $y-3=-1.5(x+5)$ and thats it...is this correct?

Answer 1

When $x=-5$ and $y=3$, we get $y'=-\dfrac{4}{3}$.

Everything else is correct, so the equation of the line only needs a minor fix. It is possible that an answer of the shape $y=mx+b$ is expected.