Find the slope of the tangent line to the curve (a lemniscate) Solution Differentiate the equation w.r.t. x, 4(2x + 2yy\')(x^2 + y^2) = 25(2x - 2yy\') Put in x = -3 and y = -1 to get 4(-6 - 2y\')(10) = 25(-6 + 2y\') Solve it to get y\' = -9/13, which is the slope of the tangent at the point (-3,-1).