Question

The equation of the smallest circle passing through the points $(2,2)$ and $(3,3)$ is

• A. $x^2+y^2+5x+5y+12=0$
• B. $x^2+y^2-5x-5y+12=0$
• C. $x^2+y^2+5x-5y+12=0$
• D. $x^2+y^2-5x+5y-12=0$

Answer 1

Answer: (B)

Let the points be $A=(2,2)$ and $B=(3,3)$. Since, the circle passing through these points, so they satisfie the equation of the circle.
Now, taking option $(b)$,
Let $S\equiv x^2+y^2-5x-5y+12=0$
At $A=(2,2)$
$2^2+2^2-5(2)-5(2)+12=0$
$\Rightarrow 0=0$
At $B=(3,3)$
$3^2+3^2-5(3)-5(3)+12=0$
$\Rightarrow 0=0$
Hence, option $(b)$ is correct.