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find the eqn of an ellipse with foci (-1,5 )AND(5,5) whose major axis is 10.?
find the eqn of a parabola with latus rectum joining the points (3,5) and (3,-3).
1 Answer
- PopeLv 77 years agoFavorite Answer
The ellipse:
The midpoint of the line segment joining the foci is the center.
center (2, 5)
Each focus is 3 units from there horizontally. The semimajor is 5.
semiminor = √(5² + 3²) = 4
(x - 2)²/25 + (y - 5)²/16 = 1
The parabola:
The midpoint, (3, 1), of the latus rectum is the focus. The length of the latus rectum is 8, and one-fourth of that (2 units) is the distance from focus to vertex.
The vertex is (1, 1) or (5, 1).
(y - 1)² = 8(x - 1)
or
(y - 1)² = -8(x - 5)
