The equation represents a circle is option (A) (x+2)^2 +(y-3)^2 = 72 is the correct answer.
What is a circle?
A circle is a collection of all points in a plane which are at a constant distance from a fixed point. A circle is a round-shaped figure that has no corners or edges.
For the given situation,
The center of the circle, (h,k) = (-2,3)
The point on the circle, (x,y) = (4,-3)
The radius of the circle is
[tex]r=\sqrt{(h-x)^{2} +(k-y)^{2} }[/tex]
⇒ [tex]r=\sqrt{(-2-4)^{2} +(3-(-3))^{2} }[/tex]
⇒ [tex]r=\sqrt{6^{2}+6^{2} }[/tex]
⇒ [tex]r=\sqrt{72}[/tex]
The formula of equation of circle is
[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]
The circle has the center (h,k) = (-2,3) and radius is √72,
⇒ [tex](x-(-2))^{2}+(y-3)^{2}=(\sqrt{72} )^{2}[/tex]
⇒ [tex](x+2)^{2}+(y-3)^{2}=72[/tex]
Hence we can conclude that the equation represents a circle is option (A) [tex](x+2)^{2}+(y-3)^{2}=72[/tex] is the correct answer.
Learn more about circles here
https://brainly.com/question/27421661
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