Question

Find the equation of the circle which touches the both axes in first quadrant and whose radius is a.

Answer 1

Clearly centre of the circle = (a, a) and radius = a

Equation of circle with radius r and centre (h, k) is (x – h)² + (y – k)² = r²

So, the equation of the required circle

⇒ (x – a)² + (y – a)² = a²

⇒ x² – 2ax + a² + y² – 2ay + a² = a²

⇒ x² + y² – 2ax – 2ay + a² = 0

Hence, the required equation is x² + y² – 2ax – 2ay + a² = 0