Find the equation of the ellipse whose center is at origin foci(1,0)and (-1,0) and ecentricity is1/2

Asked by deepakagarwal1024 | 23rd Dec, 2018, 06:32: PM

Expert Answer:

begin mathsize 12px style E q u a t i o n space o f space E l l i p s e comma space w h o s e space c e n t e r space i s space a t space o r i g i n space i s space g i v e n space b y
x squared over a squared plus y squared over b squared space equals space 1 space............ left parenthesis 1 right parenthesis
w h e r e space 2 a space a n d space 2 b space a r e space l e n g t h space o f space m a j o r space a x i s space a n d space l e n g t h space o f space m i n o r space a x i s space r e s p e c t i v e l y

f o c i space o f space e l l i p s e space a r e space left parenthesis a e comma 0 right parenthesis comma space left parenthesis negative a e space comma space 0 right parenthesis comma space w h e r e space e space i s space e c e n t r i c i t y
a e space equals space 1 space a n d space e space equals space 1 divided by 2 comma space h e n c e space a space equals space 2

e c e n t r i c i t y space e space equals space square root of fraction numerator a squared minus b squared over denominator a squared end fraction end root space o r space fraction numerator a squared minus b squared over denominator a squared end fraction space equals space 1 fourth space o r space space b squared space equals space 3
H e n c e space i f space w e space s u b s t i t u t e space a space a n d space b squared space i n space e q n. left parenthesis 1 right parenthesis space comma space w e space g e t space t h e space e l l i p s e space a s comma space space x squared over 4 plus y squared over 3 space equals 1 end style

Answered by Thiyagarajan K | 23rd Dec, 2018, 10:13: PM

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