Find the equation of the circle with centre \((-1,3)\) and radius 4 ____________
A. \(x^{2}+y^{2}-6 x+4 y=6 \) B. \(x^{2}+y^{2}+2 x-6 y=16\) C. \(x^{2}+y^{2}-6 x+2 y=16 \) D. \(x^{2}+y^{2}+2 x-6 y=6\)
Correct Answer: D
Explanation
The equation of a circle with centre \((a, b)\) and radius \(r\) is given as \((x-a)^{2}+(v-b)^{2}=r^{2}\) for \((-1,3)\) and \(r=4\) Here, \(a=-1, b=3\) So that. \({[x-(-1)]^{2}+(y-3)^{2}=4^{2} }\) \((x+1)^{2}+(y-3)^{2}=16\) \(x^{2}+2 x+1+y^{2}-6 y+9=16\) \(x^{2}+y^{2}+2 x-6 y+10=16\) \(x^{2}+y^{2}+2 x-6 y=6\)