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Question: Eccentricity of ellipse whose equation is x = 3(cos t + sin t) , y = 4(cos t – sin t) where t is par...

Eccentricity of ellipse whose equation is x = 3(cos t + sin t) , y = 4(cos t – sin t) where t is parameter:

A

12\frac{1}{2}

B

13\frac{1}{\sqrt{3}}

C

74\frac{\sqrt{7}}{4}

D

23\frac{2}{\sqrt{3}}

Answer

74\frac{\sqrt{7}}{4}

Explanation

Solution

Ellipse

(x3)2\left( \frac{x}{3} \right)^{2}+ (y4)2\left( \frac{y}{4} \right)^{2}= (cos t + sin t)2 + (cos t – sin t)2 = 2

Ž x218+y232\frac{x^{2}}{18} + \frac{y^{2}}{32} = 1

e = 1–a2b2\sqrt{1–\frac{a^{2}}{b^{2}}} = 1–1832\sqrt{1–\frac{18}{32}} = 1432\sqrt{\frac{14}{32}} = 74\frac{\sqrt{7}}{4}