Question

The equation of circle passing through $(4,5)$ and having the centre at $(2,2)$, is

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

Since centre of the circle is $(2,2)$ and the circle passes through $(4,5)$, therefore,

Radius of the circle $r=\sqrt{(4-2{)}^2+(5-2{)}^2}=\sqrt{13}$ units

Now, equation of the circle is given by, $(x-h{)}^2+(y-k{)}^2=r^2$ where $h=2,k=2$

$\Rightarrow (x-2{)}^2+(y-2{)}^2=13$

$\Rightarrow x^2+4-4x+y^2+4-4y=13$

$\Rightarrow x^2+y^2-4y-4x-5=0$