Question

Find the equation of the circle whose centre is same as the centre of the circle x2 + y2 – 6x + 4y + 9 = 0 and Passsing through the point (-2,3)

Answer 1

Given x2 + y2 – 6x + 4y + 9 = 0, & P = (-2, 3)

Centre = c(3, -2), P = (-2, 3)

r = cp = (\sqrt{(-2 - 3)^2 + (3 - (-2))^2} = \sqrt{25 + 25} )

= √50

Let equation of the required circle is

x2 + y2 – 6x + 4y + c = 0

⇒ 50 = 13 – c ⇒ c = – 37

∴ The required circle is x2 + y2 – 6x + 4y – 37 = 0.