Write the equation of the ellipse formed by foci (6,2) and (10,2) and having a minor axis of length 10.

Zackary Diaz

Zackary Diaz

Answered question

2022-11-18

Write the equation of the ellipse formed by foci (6,2) and (10,2) and having a minor axis of length 10.

Answer & Explanation

Envetenib8ne

Envetenib8ne

Beginner2022-11-19Added 17 answers

foci are
( 6 , 2 )  and  ( 10 , 2 )
hence center = = ( 6 + 10 2 , 2 + 2 2 ) = ( 8 , 2 )
clearly as y coordinate of foci is 2
i.e same for both, the axis is parallel to x-axis
Now, length of minor axis is 10
now, b 2 = a 2 ( 1 e 2 ) = a 2 a 2 e 2  so  25 = a 2 4 a 2 = 29
now equation of ellipse
( x x 1 ) 2 a 2 + ( y y 1 ) 2 b 2 = 1 ,   ( x 1 , y 1 ) = ( 8 , 2 )
Hence equation of ellipse is
( x 8 ) 2 29 + ( y 2 ) 2 25 = 1

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