Question

The equation of the circle whose centre is $(-5,4)$ and passes through the origin, is

• A. $x^2+y^2-8x+10y=0$
• B. $x^2+y^2+8x-10y+12=0$
• C. $x^2+y^2+10x-8y=0$
• D. $x^2+y^2+10x-8y+25=0$

Answer 1

The correct option is C $x^2+y^2+10x-8y=0$

The equation of a circle with centre at $(-5,4)$ is
$(x+5{)}^2+(y-4{)}^2=r^2$
Since, it passes through the origin,
$\therefore (0+5{)}^2+(0-4{)}^2=r^2\Rightarrow r^2=41$

Hence, the equation of circle is
$(x+5{)}^2+(y-4{)}^2=41\Rightarrow x^2+y^2+10x-8y=0$