Question

The equation $x^2+y^2+4x+6y+13=0$ represents

• A. a circle with radius $5\text{units}$
• B. a pair of two distinct straight lines
• C. a pair of coincident straight lines
• D. a point circle

Answer 1

The correct option is D a point circle

Given: $x^2+y^2+4x+6y+13=0$
Here, $g=2,f=3,c=13$
Radius of the circle is
$r=\sqrt{g^2+f^2-c}$
$\Rightarrow r=\sqrt{2^2+3^2-13}$
$\Rightarrow r=0$
$\therefore$ The given equation represents a point circle.