Question

Equation of the ellipse whose axes are along the coordinate axes, vertices are (± 5, 0) and foci at (± 4, 0) is ______.

Options

• `x^2/16 + y^2/9` = 1

• `x^2/25 + y^2/9` = 1

• `x^2/4 + y^2/25` = 1

• `x^2/25 + y^2/16` = 1

Answer 1

Equation of the ellipse whose axes are along the coordinate axes, vertices are (± 5, 0) and foci at (± 4, 0) is `underlinebb(x^2/25 + y^2/9 = 1)`.

Explanation:

Let the equation of the required ellipse be

`x^2/a^2 + y^2/b^2` = 1  ...(i)

The coordinates of its vertices and foci are (± a, 0) and (± ae, 0) respectively.

∴ a = 5 and ae = 4 `\implies` e = `4/5`

Now, b² = a² (1 – e²)

`\implies` b² = `25(1 - 16/25)` = 9

Substituting the values of a² and b² in (i), we get

`x^2/25 + y^2/9` = 1, which is the equation of the required ellipse.