Correct Answer - Option 4 : x

^{2} + y

^{2}- 4x + 6y - 37 = 0

__Concept:__

If Circle with **centre (h, k) **and passes through an arbitrary point **P (x, y)** on the circle, then the radius of circle,

| CP | = **r **= \(\rm \sqrt{\left ( x-h \right )^{2}+\left ( y-k \right )^{2}}\)

Equation of circle having centre (h, k) and radius r is

(x – h) 2 + (y – k) 2 = r2

__Calculation:__

Let C (2, -3) be the centre of of the given circle and let it passe through the point P (3, 4). Then, the radius of circle

| CP | = r = \(\rm \sqrt{\left ( 3-2 \right )^{2}+\left ( 4+3 \right )^{2}}\) = \(\sqrt{50}\)

∴ Required equation of circle is ,

( x - 2 )2 + ( y + 3 )2 = ( \(\sqrt{50}\) )^{2}

⇒ **x**^{2 }+ y^{2 }-** 4x + 6y - 37 = 0**.

**The correct option is 4. **