Question

Find the equation of the circle concentric with x² + y² − 4x − 6y − 3 = 0 and which touches the y-axis.

Answer 1

Since, the circles are concentric.
$\Rightarrow$Centre of required circle = Centre of x² + y² − 4x − 6y − 3 = 0

The centre of the required circle is (2, 3).

We know that if a circle with centre (h, k) touches the y-axis, then h is the radius of the circle.
Thus, the radius is 2.

∴ Equation of the circle:
${\left(x-2\right)}^2+{\left(y-3\right)}^2=2^2$
$\Rightarrow x^2+y^2-4x-6y+9=0$