Question

The equation of the circle concentric with $x^2 + y^2 + 6x + 2y + 1 = 0$ and passing through the point (-2, -1) is

• A. $x^2 + y^2 + 4x + 2y + 5 = 0$
• B. $x^2 + y^2 + 4x + 2y + 6 = 0$
• C. $x^2 + y^2 + 6x + 2y + 6 = 0$
• D. $x^2 + y^2 + 6x + 2y + 9 = 0$

Answer 1

Answer: (D)

$x^2 + y^2 + 6x + 2y + 1 = 0$
Centre of this circle is (-3, -1)
Radius of the circle having centre at (-3, -1) and passing through the point (-2, -1) is given by
$r = \sqrt{\left(-3+2\right)^{2} +\left(-1+1\right)^{2}} = 1 $
$\therefore $ Equation of circle is $\left(x+3\right)^{2} + \left(y+1\right)^{2} = 1 $
$\Rightarrow x^{2} +y^{2} + 6x +2y + 9 = 0 $.