Question

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

• A. a pair of coincident lines
• B. a pair of concurrent straight lines
• C. a parabola
• D. a point circle

Answer 1

Answer: (D)

We have,
$x^2+y^2+4x+6y+13=0$
$\Rightarrow (x^2+4x+4)-4+(y^2+6y+9)$
$-9+13=0$
$\Rightarrow (x+2{)}^2+(y+3{)}^2-13+13=0$
$\Rightarrow (x+2{)}^2+(y+3{)}^2=0$
which is equation of a point circle.