The equation of the ellipse having foci (0, 1), (0, –1) and minor axis of length 1 is_________ .

Question

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The equation of the ellipse having foci (0, 1), (0, –1) and minor axis of length 1 is_________ .

Answer 1

Foci = (0, ±ae) = (0, ±1)

be = 1

Minor Axis = 2a = 1, a = 0.5

a² = b² (1 - e² )

(0.5)² = b² (1 - e²)

0.25 = b² - b²e²

0.25 = b² - 1 {As be = 1}