Question

Which equation represents a circle with a center point of (-2,3) that passes through the point (4, -3)?

PLEASE HELP ASAP IM GIVING BRAINLIEST

Answer 1

Answer:

$A) (x+2)^{2} +(y-3)^{2} =72$

Step-by-step explanation:

$Radius=\sqrt{(4+2)^{2}+(-3-3)^{2} }$

$=\sqrt{6^{2} +6^{2} } =6\sqrt{2 }$

$equation:$

$(x+2)^{2}+(y-3)^{2} =(6\sqrt{2}^{2})$

$(x+2)^{2}+(y-3)^{2} =72$

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Answer 2

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

$r=\sqrt{(h-x)^{2} +(k-y)^{2} }$

⇒ $r=\sqrt{(-2-4)^{2} +(3-(-3))^{2} }$

⇒ $r=\sqrt{6^{2}+6^{2} }$

⇒ $r=\sqrt{72}$

The formula of equation of circle is

$(x-h)^{2}+(y-k)^{2}=r^{2}$

The circle has the center (h,k) = (-2,3) and radius is √72,

⇒ $(x-(-2))^{2}+(y-3)^{2}=(\sqrt{72} )^{2}$

⇒ $(x+2)^{2}+(y-3)^{2}=72$

Hence we can conclude that the equation represents a circle is option (A) $(x+2)^{2}+(y-3)^{2}=72$ is the correct answer.

Learn more about circles here

https://brainly.com/question/27421661

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