Find an equation of the tangent line to the curve

2(x2+y2)2=25(x2−y2)

(a lemniscate) at the point (3,1). Please help.

1 answer

take the derivative...
2(x^2+y^2+2xy)=25(x^2-y^2)
2(2x dx + 2ydy+2ydx+2xdy=25(2xdx-2ydy)

collect the dy terms

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

dy/dx= you do it, then put in the point 3,1 and solve for dy/dx