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Question
Find the equation for the ellipse that satisfies the given conditions:
Centre at (0, 0), major axis on the y-axis and passes through the points (3, 2) and (1, 6)
Solution
`x^2/b^2 + y^2/a^2 = 1`
At point (3, 2), `9/b^2 + 4/a^2 = 1` .....(i)
And at point (1, 6), `1/b^2 + 36/a^2 = 1` ......(ii)
Multiplying equation (i) by 9, we get `81/b^2 + 36/a^2 = 9`
By subtracting equation (ii) from this,
`80/b^2 = 8` or `b^2 = 80/8 = 10`
Putting the value of b2 in equation (i),
`9/10 + 4/a^2 = 1`
or `4/a^2 = 1 - 9/10 = 1/10`
∴ a2 = 40
equation of ellipse,
`x^2/10 + y^2/40 = 1`
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