Step #1 Make sure the point is on the curve. Please demonstrate this.
Step #2 Use your Implicit Differentiation skills. This requires a nice understanding fo the Chain Rule
For the first term, I get -4x <== Just the good old polynomial rule there.
For the second term, I get -x*(dy/dx) - y <== A thing of beauty. Product rule and chain rule.
You do the third term and the other side of the equal sign.
Step #3 Find dy/dx
Step #4 Evaluate dy/dx at the given point (assuming it is on the curve).