Question

If a circle passes through the point (0, 0) (a, 0), (0, b) then find the coordinates of its centre.

Answer 1

Given points are (0, 0), (a, 0) and (0, b)

General equation of the circle is x² + y² + 2gx + 2fy + c = 0

Where the centre is (– g, – f) and radius = `sqrt(g^2 + f^2 - c)`

If it passes through (0, 0)

∴ c = 0

If it passes through (a, 0) and (0, b)

Then a² + 2ga + c = 0

⇒ a² + 2ga = 0    .....[∵ c = 0]

∴ g = ` - a/2`

And 0 + b² + 0 + 2fb + c = 0

⇒ b² + 2fb = 0  ......[∵ c = 0]

⇒ f = `- b/2`

Hence, the coordinates of centre of the circle are (– g, – f) = `(a/2, b/2)`