Question

The equation of a circle with centre $(2,2)$ and passes through the point $(4,5)$ is

• A. $x^2+y^2+4x-4y-5=0$
• B. $x^2+y^2-4x+4y-5=0$
• C. $x^2+y^2-4x-4y+5=0$
• D. $x^2+y^2-4x-4y-5=0$

Answer 1

The correct option is D $x^2+y^2-4x-4y-5=0$

Equation of circle
$(x-2{)}^2+(y-2{)}^2=r^2$
Circle passes through the point $(4,5)$
$(4-2{)}^2+(5-2{)}^2=r^2\Rightarrow r^2=4+9=13$

So, the equation of circle
$(x-2{)}^2+(y-2{)}^2=13\Rightarrow x^2+y^2-4x-4y-5=0$