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Find the equation of the circle with center that passes through point A. center (-5, -5) and point A (3, 1)

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Answer:

(x + 5)² + (y + 5)² = 10²

Step-by-step explanation:

The line drawn from the centre of a circle to any point on the circumference is called a radius.

Therefore, the radius =

[tex] \sqrt{ {(3 - ( - 5))}^{2} + {(1 - ( - 5))}^{2} } [/tex]

[tex] = \sqrt{ {(3 + 5)}^{2} + {(1 + 5)}^{2} } [/tex]

[tex] = \sqrt{ {8}^{2} + {6}^{2} } [/tex]

[tex] = \sqrt{64 + 36} [/tex]

[tex] = \sqrt{100} [/tex]

r = 10

General equation of a circle:

(x - a)² + (y - b)² = r², where (a,b) is the coordinate of the centre.

Since (-5, -5) is the centre,

(x - (-5))² + (y - (-5))² = 10²

(x + 5)² + (y + 5)² = 10²

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