What is the slope of the tangent line at the point (-3,-1) for the equation 2(x^2+y^2)^2=25(x^2-y^2)?

Question

using implicit diferentiation can you help me solve this with steps please

Answer 1

First simplify algebraically:
2(x^4+2*x^2*y^2+y^4)
=25x^2-25y^2

2x^4+2y^4+4x^2*y^2
-25x^2+25y^2 = 0

Differentiate both sides with respect to x using the chain rule:

8x^3+2y^4(dy/dx)+8x*y^2(dy/dx)
-50x+25y^2(dy/dx) = 0

Solve for (dy/dx) algebraically:

Plug in x = -3 and y = -1 to find the numerical value of (dy/dx), the slope of the tangent line:

The answer should be: 22