Can't get this implicit differentiation I've been working at this implicit differentiation problem for a little over an hour now, and I, nor my friends can figure it out. The question reads "Find the equation of the tangent line to the curve (a lemniscate) $2(x^2+y^2)^2=25(x^2−y^2)$ at the point (3,1). Write the equation of the tangent line in the form $y=mx+b.$"
Every time that we do it we get a ridiculous number for the slope (${150}/{362}$)

Let's consider $y$ to be a function of $x$ (usually written "$y=y(x)$") for $x$ close to $3$. Then
$$2(x^2+y(x)^2)^2=25(x^2-y(x)^2)$$
so by differentiating on $x$ (using basically the chain rule), we obtain
$$4(x^2+y(x)^2)(2x+2y(x)y'(x))=25(2x-2y(x)y'(x))$$
Substitute $x=3$ and $y(x)=y(3)=1$, and you will find the value of $y'(3)=-9/13$ (at least that's what I found). This means that the slope of the tangent is $-9/13$, so the equation for the tangent is
$$y=y(3)+y'(3)(x-1)=1-(9/13)(x-1)=-\frac{9}{13}x+22/13$$
