Question

The equation of the circle which passes through the point $(4, 5)$ and has its centre at $(2, 2)$ is

• A. $(x - 2) + (y - 2) = 13$
• B. $(x - 2)^2 + (y - 2)^2 = 13$
• C. $(x)^2 + (y)^2 = 13$
• D. $(x - 4)^2 + (y - 5)^2 = 13$

Answer 1

Answer: (B)

$(x - 2)^2 + (y - 2)^2 = 13$

Answer 2

As the circle is passing through the point $(4, 5)$ and its centre is $(2, 2)$ so its radius is
$\sqrt{\left(4-2\right)^{2} + \left(5-2\right)^{2}} = \sqrt{13}$
$\therefore$ The required equation is :
$\left(x-2\right)^{2} +\left(y-2\right)^{2} = 13$