Ellipse: The locus of points for which the sum of the distances from two foci F and F′ is constant (2a).
Standard form x²/a² + y²/b² = 1 (a > b > 0):
・Vertices (±a, 0), (0, ±b) ・Foci (±c, 0), c² = a² − b²
Example ① Find the foci of x²/25 + y²/9 = 1.
Solution:a=5, b=3, c²=25−9=16, c=4。Foci (±4, 0)
Solution:a=5, b=3, c²=25−9=16, c=4。Foci (±4, 0)
Key Point
- Major axis = 2a, minor axis = 2b
- Eccentricity e = c/a (0 < e < 1)
Practice Problems
- Find the foci of x²/16 + y²/25 = 1.
Answers and Explanations
- Answer:(0, ±3)
A vertically elongated ellipse. a=5, b=4, c=3。