find the equation of the ellipse whose centre is at (0,0) and major axis on y axis and passes through the pointd (3,2) and (1,6)

Asked by gargpurvi85 | 28th Feb, 2015, 08:16: PM

Expert Answer:

G i v e n space t h a t space t h e space c e n t r e space o f space t h e space e l l i p s e space i s space t h e space o r i g i n space a n d space m a j o r space a x i s space y minus a x i s. T h u s space t h e space s tan d a r d space e q u a t i o n space o f space t h e space e l l i p s e space i s x squared over a squared plus y squared over b squared equals 1 comma space w h e r e comma space b greater than a S i n c e space t h e space e l l i p s e space i s space p a s sin g space t h r o u g h space t h e space p o i n t space open parentheses 3 comma 2 close parentheses space a n d space open parentheses 1 comma 6 close parentheses comma space w e space h a v e comma 3 squared over a squared plus 2 squared over b squared equals 1 space a n d space 1 squared over a squared plus 6 squared over b squared equals 1 rightwards double arrow 9 over a squared plus 4 over b squared equals 1 space a n d space 1 over a squared plus 36 over b squared equals 1.... left parenthesis 1 right parenthesis N o w space c o n s i d e r comma space 1 over a squared equals alpha space a n d space 1 over b squared equals beta T h u s space s u b s t i t u t i n g space t h e space v a l u e s space o f space 1 over a squared space a n d space 1 over b squared i n space e q u a t i o n s space left parenthesis 1 right parenthesis comma space w e space h a v e comma 9 alpha plus 4 beta equals 1 space a n d space alpha plus 36 beta equals 1 S o l v i n g space t h e space a b o v e space e q u a t i o n s comma space w e space h a v e comma alpha equals 1 over a squared equals 1 over 10 space a n d comma space beta equals 1 over b squared equals 1 over 40 T h u s space t h e space e q u a t i o n space o f space t h e space e l l i p s e space i s space x squared over 10 plus y squared over 40 equals 1

Answered by Vimala Ramamurthy | 1st Mar, 2015, 11:59: AM