As shown above, the ellipse has equation: , and point is the center of the circle: If is a point on ellipse , both pass through and they are both tangent to circle , and the product of the slope of is equal to , then find the all possible coordinate(s) of point .
How to submit:
First, find the number of all possible solutions. Let denote the number of solutions.
Then Sort the solutions by x-coordinate from smallest to largest, if the x-coordinate is the same, then sort by y-coordinate from smallest to largest.
Let the sorted solutions be: , then .
For instance, if the solution is:
Then the sorted solution will be:
Then , .
For this problem, submit .
Have a look at my problem set: SAT 1000 problems