Need Help, thank you

Question

Which of the following is true about the graph of x squared plus x over y minus y squared equals 1 at the point (−2, 1)?

a. y ′ does not exist at (−2, 1), and the slope of the tangent line at that point is undefined

b. y ′ does not exist at (−2, 1), and the slope of the tangent line at that point is zero

c. y ′ does exist at (−2, 1), and the slope of the tangent line at that point is zero

Answer 1

The way I would go about this is to take the derivative with respect to y with x being treated as a constant. Starting from x²+x/y+y² we apply d/dy, we must treat x as a constant here with x² deriving to zero because it is constant with respect to y the derivative of x/(y-y²) evaluates to -x(2y-1)/(y-y²) squared using the quotient or reciprocal rule (lo*dhi-hi*dlo)/(lo*lo) and y² of course evaluates to 2y and y evaluates to 1 in the top part of the fraction. Putting it all together we get -x(/(y² -y²)².

Following the inputs the only answer that works is a because the denominator turns into (1 - -1²) which is really just 1-1 = 0 and a 0 in the denominator is undefined which singles out a as the answer. I hope this helps!