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 $S \equiv x^{2}+y^{2}-5 x-5 y+12=0$
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.