Question

If x² + (2h - 1)xy + y² - 24x - 8y + k = 0 is the equation of the circle and 12 is the radius of the circle, then ______.

Options

• h = `1/2`, k = - 16

• h = 2, k = 10

• h = `1/2`, k = 16

• h = 2, k = - 10

Answer 1

If x² + (2h - 1)xy + y² - 24x - 8y + k = 0 is the equation of the circle and 12 is the radius of the circle, then h = `1/2`, k = 16.

Explanation:

The given equation represents a circle, if coefficient of xy = 0.

∴ 2h - 1 = 0  ⇒ h = `1/2`

and `sqrt((- 12)^2 + (- 4)^2 - "k")` = 12

⇒ 160 - k = 144

⇒ k = 16