Find the slope of the tangent line (ii)

[cal.queen92]

Homework Statement

Find the slope of the tangent line to the curve:

2(x^2 + y^2)^2 = 25(x^2 - y^2)

at the point (-3, -1)

Homework Equations

Implicit differentiation

The Attempt at a Solution

2(x^2 + y^2)^2 = 25(x^2 - y^2)

1. 4(x^2 + y^2)(2x + 2y(dy/dx)) = 25(2x - 2y(dy/dx))

2. (4x^2 + 4y^2)(2x + 2y(dy/dx)) = 50x - 50y(dy/dx)

3. 8x^3 + 8x^2*y(dy/dx) + 8xy^2 + 8y^3(dy/dx) = 50x - 50y(dy/dx)

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

5. therefore: dy/dx = (50x - 8x^3 - 8xy^2)/(8x^2*y + 8y^3 + 50y)

then when i plug in the values of x and y, i obtain an answer of -3, but this is incorrect!

Can anyone see where I am going wrong?

Thanks!

 

[quantumdude]

Your arithmetic must be wrong. When I plug your numbers into your derivative I get -9/13.