Question

At which point does the circle x² + y² - 4x - 6y + 4 = 0 touch the x-axis?

Answer 1

For touching x-axis, put y = 0 in equation of circle, we obtain

x² - 4x + 4 = 0

⇒ (x - 2)² = 0

⇒ x - 2 = 0

⇒ x = 2

Hence, circle x² + y² - 4x - 6y + 4 = 0 touches x-axis at point (2, 0).