Question

Find the equation of circles that touch both the axes and pass through (− 4, −2) in general form

Answer 1

Since the circle touches both the axes

Its centre will be (r, r) and the radius will be r.

Here centre = C = (r, r) and point on the circle is A = (− 4, −2)

CA = r

⇒ CA² = r²

(i.e) (r + 4)² + (r + 2)² = r²

⇒ r² + 8r +16 + r² + 4r + 4 – r² = 0

(i.e) r² + 12r + 20 = 0

(r + 2)(r + 10) = 0

⇒ r = − 2 or − 10

When r = − 2, the equation of the circle will be (x + 2)² + (y + 2)² = 2²

(i.e) x² + y² + 4x + 4y + 4 = 0

When r = −10, the equation of the circle will be (x + 10)² + (y + 10)² = 10²

(i.e) x² + y² + 20x + 20y + 100 = 0