1. The equation of an ellipse with center in the origin is
2. The coordinates of the given point satisfy the equation of the ellipse:
3. The distance of a focus to the center is
4. According to the question you have to solve the system of equations:
5. From the 1st equation you'll get:
Sub in this term into the 2nd equation to replace bČ:
This looks a little bit terrifying. I'll show you the first steps.
Under the assumption that a must be positive, you can do:
Now square both sides and solve for a. The only valid solution is , consequently and f = 2. That means the given point is the endpoint of the latus rectum.