Question

A circle has radius 3 units and its centre lies on the line y = x – 1. If it passes through the point (7, 3), its equation is ______.

Answer 1

A circle has radius 3 units and its centre lies on the line y = x – 1. If it passes through the point (7, 3), its equation is x² + y² – 8x – 6y + 16 = 0.

Explanation:

Let (h, k) be the centre of the circle.

Then k = h – 1.

Therefore, the equation of the circle is given by (x – h)² + [y – (h – 1)]² = 9  ......(1)

Given that the circle passes through the point (7, 3)

And hence we get (7 – h)² + (3 – (h – 1))² = 9

or (7 – h)² + (4 – h)² = 9

or h² – 11h + 28 = 0

Which gives (h – 7)(h – 4) = 0

⇒ h = 4 or h = 7

Therefore, the required equations of the circles are x² + y² – 8x – 6y + 16 = 0.

or x² + y² – 14x – 12y + 76 = 0