You sure you got the curve C right. Completing the square in gives
There are no real solutions to this equation.
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
This is the way I would do it. Suppose the point on the circle is Then satisfies
.
The tangent to the curve at this point is
and the slope of the line connecting to is
These must equal, hence
or
You are required to find the distance between the two points or
Now gives
so
Edit: Earthboth's solution is so much more elegant (and of course easier!)