An ellipse in the first quadrant is tangent to both the x-axis and y-axis. One focus is at (3, 7) and the other focus is at (d, 7). Compute d.
If the first foci is (3,7) and the second is (d,7), then C= (d+32,7). C is the center of the ellipse. The point where the ellipse touches the x-axis is (d+32,0).
We know that P(any points on the ellipse) = T, so
2√(d−32)2+72=d+3
√(d−32)2(4)+72(4)=d+3
√(d−3)2+196=d+3
Then, by squaring both sides, we get
(d−3)2+196=d2+6d+9
d2−6d+9+196=d2+6d+9
12d=196
d=493
- Daisy