Question

Find the equation for the ellipse that satisfies the given conditions:

Major axis on the x-axis and passes through the points (4, 3) and (6, 2).

Answer 1

Let the equation of ellipse be `x^2/a^2 + y^2/b^2 = 1`

It goes through the points (4, 3) and (6, 2)

`16/a^2 + 9/b^2 = 1`     ...(i)

`36/a^2 + 4/b^2 = 1`     ...(ii)

On multiplying equation (i) by 4 and equation (ii) by 9

`64/a^2 + 36/b^2 = 4`   ...(iii)

`324/a^2 + 36/b^2`       ...(iv)

By subtracting equation (iii) from equation (iv),

`260/a^2 = 5`

or `a^2 = 260/52`

Putting the value of a² in equation (i),

`16/52 + 9/b^2 = 1`

or `9/b^2 = 1 - 16/52 = 36/52`

`9/b^2 = 36/52`

or `b^2 = (9 xx 52)/36 = 13`

∴ Equation of ellipse, `x^2/52 + y^2/13 = 1`.