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)

Answer 1

`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`