Exercise 11.1 In each of the following Exercises 1 to 5, find the equation of the circle with Question 1. centre (0, 2) and radius 2 Solution: Here h = 0,k = 2 and r = 2 The equation of circle is, (x-h) 2 + (y- k) 2 = r 2 ∴ (x – 0) 2 + (y – 2) 2 = (2) 2 ⇒ x 2 + y 2 + 4 – 4y = 4 ⇒ x 2 + y 2 – 4y = 0 Question 2. centre (-2,3) and radius 4 Solution: Here h=-2,k = 3 and r = 4 The equation of circle is, (x – h) 2 + (y – k) 2 = r 2 ∴(x + 2) 2 + (y – 3) 2 = (4) 2 ⇒ x 2 + 4 + 4x + y 2 + 9 – 6y = 16 ⇒ x 2 + y 2 + 4x – 6y – 3 = 0 Question 3. centre and radius Solution: here h = , k = and r = The equation of circle is, Question 4. centre (1, 1) and radius Solution: Here h = l, k=l and r = The equation of circle is, (x – h) 2 + (y – k) 2 = r 2 ∴ (x – 1) 2 + (y – 1) 2 = 2 ⇒ x 2 + 1 – 2x + y 2 +1 – 2y = 2 ⇒ x 2 + y 2 – 2x – 2y = 0 Question 5. centre (-a, -b) and radius . Solution: Here h=-a, k = -b and r = The equation of circle is, (x – h) 2 + (y – k) 2 = r 2 ∴