Find the equation of the circle with centre (- a, - b) and radius √a² + b²

Solution:

The equation of a circle with centre(h, k) and radius r is given as

(x - h)² + (y - k)² = r²

It is given that centre (h, k) = (- a, - b)

and radius (r ) = √a² + b².

Therefore, the equation of the circle is

(x - a)² + (y - b)² = (√a² + b²)²

x² + 2ax + a² + y² + 2by + b² = a² - b²

x² + y² + 2ax + 2by + 2b² = 0

NCERT Solutions Class 11 Maths Chapter 11 Exercise 11.1 Question 5

Find the equation of the circle with centre (- a, - b) and radius √a² + b²

Summary:

The equation of the circle is  x² + y² + 2ax + 2by + 2b² = 0