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Find the equation of the ellipse referred to its major and minor axes as the coordinate axes x, y respectively with latus rectum of length 4 and the distance between foci 4√2. |
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Answer» Let the equation of the ellipse is x2/a2 + y2/b2 = 1 (a > b) Length of the latus rectum = 2b2/a2 = 4 ⇒ b2 = 2a. Foci are S (ae, 0), S' (– ae, 0) Distance between the foci = 2ae = 4√2 ae = 2√2 b2 = a2 (1 – e2) = a2 – (ae)2 2a = a2 – 8 ⇒ a2 – 2a – 8 = 0 (a – 4) (a + 2) = 0 a = 4 or – 2 a > 0 ⇒ a = 4 b2 = 2a = 2. 4 = 8 Equation of the ellipse is x2/a2 + y2/b2 = 1 x2/16 + y2/8 = 1 x2 + 2y2 = 16 |
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