Implicit Differentiation with a Tangent Line

Question

I was looking to implicitly differentiate $$-22x^6+4x^{33}y+y^7=-17$$ and found it to be $$\dfrac{dy}{dx}=\dfrac{132x^5-132x^{32}y}{4x^{33}+7y^6}$$Now, I am trying to find the equation of the tangent line to the curve at the coordinate (1,1). So I then plug both 1 in for x and y into the above equation and come up with $$\dfrac{0}{11}$$Now I go to solve $$y-y1=m(x-x1)$$ getting $$y-1=0(x-1)$$ resulting in $y=1$ and the equation to be $y=x+1$ for my final answer. Am I going about this in the correct manner?

Answer 1

Your work is fine but since $m=\left(\frac{dy}{dx}\right)_{(1,1)}=0$ we have

$$y-y_1=m(x-x_1)=0 \implies y=1$$

Answer 2

your calculations for the slope of tangent are correct. The only point that you have missed is the last step of finding the equation of tangent line which is simply $y=1$ not $y=x+1$