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
⇒ x2 + y2 - 4x + 6y - 37 = 0.
The correct option is 4.