Precalculus · G-GPE
Ellipse — Standard Form, Foci, and Key Features
(x−h)²/a² + (y−k)²/b² = 1. Foci at (h±c, k) where c² = a²−b² (horizontal major axis). Vertices at (h±a, k) and co-vertices at (h, k±b).
PrecalculusCommon Core HSG-GPE.A.3G-GPEVerified correct ✓
Worked examples
For the ellipse (x + 2)²/25 + (y + 2)²/16 = 1, find the length of the semi-minor axis (b).
Answer: 4
For the ellipse (x − 2)²/25 + (y + 4)²/9 = 1, find the focal distance c. Use the formula c² = a² − b². Round to 5 decimal places.
Answer: 4
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