Question

For what value of k, the points (0, 0), (1, 3), (2, 4), and (k, 3) are concyclic?

Options

• 4

• 9

• 6

• 8

Answer 1

9

Explanation:

The equation of circle through points (0, 0), (1, 3) and (2, 4) is

x² + y² - 10x = 0

Point (k, 3) will be on the circle, if

k² + 9 - 10k = 0

⇒ k² - 10k + 9 = 0

⇒ k² - 9k - k + 9 = 0

⇒ (k - 1) (k - 9) = 0

⇒ k = 1 or k = 9