Question

Find the equation of the circle passing through the points 

(i) (0, 0), (5, 0) and (3, 3) 

(ii) (1, 2), (3, - 4) and (5, - 6) 

(iii) (20, 3), (19, 8) and (2, - 9) 

Also, find the centre and radius in each case.

Answer 1

(i) The required circle equation

(ii) The required circle equation

⇒ x² + y² - 22x - 4y - 25 = 0 is the equation with centre = (11,2)

Radius = \(\sqrt{g^2+f^2-c}\)

= \(\sqrt{(-11)^2+(-2)^2-25}\) = 10

(iii) The required circle equation

⇒ 102(x² + y²) - 1428x -612y - 11322 = 0

⇒ x² + y² - 14x - 6y - 111 = 0 is the equation with centre = (7, 3)

Radius = \(\sqrt{g^2+f^2-c}\) = \(\sqrt{(-7)^2+(-3)^2-(-111)}= 13\)