Curve's point A tangent line passes through a point P. What is the distance of AP

Let A be a point on the curve C: . If the tangent line at A passes through P(4,3), then the length of AP is?

So i'm stuck midway at the solution for this one.

So far I've gotten these equations

; the tangent line slope at any point on the curve (by implicit differentiation)

; the slope at point P; acquired by y-k=m(x-h)

and when I put those two equations together I get:

And when I input this equation back into the original curve i end up with

x= -y

I'm stuck at this point because when I plug in the last equation back to original curve again, I'm getting an complex solution.

Help please!

Oh Gosh. I am sorry. That's supposed to be