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Find the equation of the ellipse whose c...

Find the equation of the ellipse whose centre is at origin, focus is (0,4) and major axis is 10.

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Focus (0,4) is on y-axis `:." "bgta`
Major axis =2b=10
`rArr" "b=5`
Co-ordinates of focus = (0,4)
`rArr" "b*e=4`
`rArr" "e=(4)/(5)`
`:." "a^(2)=b^(2)(1-e^(2))`
`=25(1-(16)/(25))=9`
Now, equation of ellipse `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1`
`rArr" "(x^(2))/(9)+(y^(2))/(b^(2))=1`
`rArr" "25x^(2)+9y^(2)=225`.
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