Question

(x – 1)² + (y – 2)² = `(3(2x + 3y + 2)^2)/13`represents hyperbola whose eccentricity is ______.

Options

• `sqrt(13)/sqrt(3)`

• `sqrt(13)/3`

• `sqrt(3)`

• 3

Answer 1

(x – 1)² + (y – 2)² = `(3(2x + 3y + 2)^2)/13` represents hyperbola whose eccentricity is `underlinebb(sqrt(3))`.

Explanation:

`"Distance of P from the fous"/"Distance of P from the directrix"` = eccentricity

Here P is (x, y); focus is (1, 2)

∴ (x – 1)² + (y – 2)² = `(3(2x + 3y + 2)^2)/13`

⇒ Taking square root both sides, we get

`sqrt((x - 1)^2 + (y - 2)^2) = sqrt(3)/sqrt(13)(2x + 3y + 2)`

⇒ `sqrt((x - 1)^2 + (y - 2)^2)/(((2x + 3y - 2))/sqrt(13)) = sqrt(3)`

∴ e = `sqrt(3)`