This is practically the same problem I answered before. You can use the same method to find the points, then use the distance formula to find the distance between them.
Let's do this one. I may have inadvertently made some typos in the last post. The result is correct, though.
Let p be a point on :
Let q be a point on :
The slope of P is
The slope of Q is
Therefore, .......[1]
The slope from P to Q is
This has to be the slope at P (or Q):
Sub in [1]:
Now, solve for p and q. You can get points and find the distance between them.
This is how I always went about these 'line tangent to two points' problems. Maybe you can find another way.