Find the slope of the tangent line to the curve

Question

Find the slope of the tangent line to the curve (a lemniscate)

2(x²+y²)²= 25(x²-y²)

at the point (-3,-1)

m=

Answer 1

Hi Dalia,

 

You need to calculate dy/dx at (-3,-1)

 

Differentiating the given expression we get,

 

2*2(x^2+y^2)(2x+2y*dy/dx) = 25(2x-2y*dy/dx) 

 

Substituting y and x as -3 and -1 respectively, we get

 

4(9+1)(-6-2*dy/dx) = 25(-6+2*dy/dx)

 

On solving we get,

 

dy/dx = -8/13