Question

Let the ellipse `x^2/a^2 + y^2/b^2` = 1 has latus sectum equal 8 units – if the ellipse passes through   `(sqrt(5), 4)` Then The radius of the directive circle is ______.

Options

• `5sqrt(3)`

• `3sqrt(5)`

• `sqrt(15)`

• 15

Answer 1

Let the ellipse `x^2/a^2 + y^2/b^2` = 1 has latus sectum equal 8 units – if the ellipse passes through   `(sqrt(5), 4)` Then The radius of the directive circle is `underlinebb(3sqrt(5))`.

Explanation:

`(sqrt(5), 4)` lie, on `x^2/9^2 + y^2/5^2` = 1

⇒ `5/a^2 + 16/b^2` = 1  ...(1)

Latus rectum = 8 = `(2b^2)/a`

⇒ b² = 4a  ...(2)

From (1) and (2)

`5/a^2 + 4/a` = 1

⇒ a² – 4a – 5 = 0

⇒ a = 5

∴ b² = 20, a² = 25

∴ Radium of director circle is = `sqrt(a^2 + b^2)` = `3sqrt(5)`