Question

The equation of the circle concentric with the circle x² + y² - 6x - 4y - 12 = 0 and touching the Y-axis is ______.

Options

• x² + y² - 6x - 4y + 4 = 0

• x² + y² - 6x - 4y + 9 = 0

• x² + y² - 6x - 4y - 4 = 0

• x² + y² - 6x - 4y - 9 = 0

Answer 1

The equation of the circle concentric with the circle x² + y² - 6x - 4y - 12 = 0 and touching the Y-axis is x² + y² - 6x - 4y + 4 = 0.

Explanation:

Given equation of circle

x² + y² - 6x - 4y - 12 = 0      ...(i)

Centre of circle (i) Is (3, 2)

Equation of circle concentric with circle (i) and touching the Y-axis is

(x - 3)² + (y - 2)² = (3)² 

⇒ x² + 9 - 6x + y² + 4 - 4y = 9

⇒ x² + y² - 6x - 4y + 4 = 0