Find the equation for the ellipse that satisfies the given conditions: Centre at (0, 0), major axis on the yaxis and passes through the points (3, 2) and (1, 6).

Explanation

Centre is (0,0)
Let equation of ellipse is :
`(x^(2))/(a^(2))+(y^(2))/(b^(2))=1` . . . (1)
`:.(3^(2))/(a^(2))+(2^(2))/(b^(2))=1rArr(9)/(a^(2))+(4)/(b^(2))=1` . . .(2)
Ellipse passes through the point (1,6).
`:.(1^(2))/(a^(2))+(6^(2))/(b^(2))=1rArr(1)/(a^(2))+(36)/(b^(2))=1`
`rArr(9^(2))/(a^(2))+(324)/(b^(2))=9` . . . (3)
Subtracting equation (2) from equation (3)
`(320)/(b^(2))=8rArrb^(2)=40`
Put the value of `b^(2)` in equation (2)
`(9)/(a^(2))+(4)/(40)=1`
`rArr(9)/(a^(2))=1-(1)/(10)=(9)/(10)rArra^(2)=10`
From equation (1), equation jof ellipse
`(x^(2))/(10)+(40)/(b^(2))=1`