The equation of the ellipse whose centre is at origin major axis is along x axis with eccentricity 3...........

Mathematics (NDA) Coordinate Geometry

The equation of the ellipse whose centre is at origin, major axis is along x-axis with eccentricity 3 / 4 and latus rectum 4 units is -

x² / 1024 + 7y² / 64 = 1

49x² / 1024 + 7y² / 64 = 1

. 7x² / 1024 + 49y² / 64 = 1

x² / 1024 + y² / 64 = 1

Latus rectum = 4 and e = ¾ ∴

b² = 2a and c = e a

Also a² = b²+ c²

Or a² = 2 a + 9 / 16 a²

Or a = 32/7

∴ b² = 64/7

Equation of ellipse is 49x² / 1024 + 7y² / 64 = 1

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