In the ellipse 25x2 + 9y2 – 150x – 90y + 225 = 0

G i v e n e l l i p s e 25 x 2 + 9 y 2 - 150 x - 90 y + 225 = 0 ⇒ 25 ( x 2 - 6 x ) + 9 ( y 2 - 10 y ) + 225 = 0 ⇒ 25 ( x - 3 ) 2 + 9 ( y - 5 ) 2 = 225 ⇒ ( x − 3 ) 2 9 + ( y − 5 ) 2 25 = 1 ( a < b ) w h e r e a 2 = 9 , b 2 = 25 , c e n t r e ( C ) = ( 3 , 5 ) a n d e = 4 5 N o w be = 4 f o c i a r e ( h , k ± b e ) = ( 3 , 5 ± 4 ) S(3,1) ; S 1 (3,9)

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In the ellipse 25x² + 9y² – 150x – 90y + 225 = 0

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An Intiative by Sri Chaitanya

foci are at (3, 1), (3, 9)

major axis is 6

centre is (5, 3)

e = 4/5

answer is A, B.

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Detailed Solution

$G i v e n e l l i p s e 25 x^{2} + 9 y^{2} - 150 x - 90 y + 225 = 0 \Rightarrow 25 (x^{2} - 6 x) + 9 (y^{2} - 10 y) + 225 = 0 \Rightarrow 25 {(x - 3)}^{2} + 9 {(y - 5)}^{2} = 225 \Rightarrow \frac{(x - 3)^{2}}{9} + \frac{(y - 5)^{2}}{25} = 1 (a < b) w h e r e a^{2} = 9, b^{2} = 25, c e n t r e (C) = (3, 5) a n d e = \frac{4}{5} N o w be = 4 f o c i a r e (h, k \pm b e) = (3, 5 \pm 4)$
S(3,1) ; S¹(3,9)