[tex](x + 27)^2 + (y - 120)^2 = 15129[/tex]
Solution:
The equation of a circle is given as:
[tex](x-a)^2+(y-b)^2=r^2[/tex]
Where,
(a, b) is the centre of the circle
r is the radius
We have the centre of the circle (-27, 120)
Therefore,
a = -27
b = 120
Given that, it passes through origin. which means, (x, y) = (0, 0)
Substitute (a, b) = (-27, 120) and (x, y) = (0, 0) in eqn
[tex](0 + 27)^2 + (0 - 120)^2 = r^2\\\\729 + 14400 = r^2\\\\r^2 = 15129[/tex]
Substitute [tex]r^2[/tex] = 15129 and (a, b) = (-27, 120) in eqn
[tex](x + 27)^2 + (y - 120)^2 = 15129[/tex]
Thus the equation of circle is found
