What Is The Standard Equation Of A Circle That Has A Center Of (-8, 4) And Contains (-4,2)

What is the standard equation of a circle that has a center of (-8, 4) and contains (-4,2)

 

Answer:

(x + 8)² + (y - 4)² = 20

Step-by-step explanation:

First find the radius from the center (-8, 4) to the point (-4, 2) on a circle using the distance formula:

Distance = \sqrt{(x_{2}-x_{1}) ^{2} + (y_{2}- y_{1}) ^{2} }

Distance = Radius

Radius = \sqrt{(2-4)^{2}+(-4-(-8))^{2} }

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

Radius = \sqrt{4+16} =\sqrt{20} =\sqrt{(4)(5)}

Radius = 2√5

Standard Equation Center-Radius Form:

(x-h)² + (y-k) = r²

Center (h, k): (-8, 4)

Radius: 2√5

(x - (-8))² + (y - 4)² = (2√5)²

(x + 8)² + (y - 4)² = (4)(5)

(x + 8)² + (y - 4)² = 20

 


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