Which is an equation of a circle with center (-5, -7) that passes through the point (0, 0)?

a. (x - 5)2 + (y - 7)2 = 74
b. (x + 5)2 + (y + 7)2 = 37
c. (x + 5)2 + (y + 7)2 = 74
d. (x - 5)2 + (y - 7)2 = 37

The equation of the circle is (x + 5) ² + (y + 7)² = 74 .

Option (C) is correct .

Step-by-step explanation:

The general equation of the circle is given by

(x - h) ² + (y - k)² = r²

Where (h,k) are the centre of the circle and r is the radius of the circle .

As given

A circle with center (-5, -7) that passes through the point (0, 0) .

As

Put in the equation

As center of the circle is (-5, -7) and r² is 74 .

Put in the general form of the equation .

(x -(-5)) ² + (y - (-7))² = 74

(x + 5) ² + (y + 7)² = 74

Therefore the equation of the circle is (x + 5) ² + (y + 7)² = 74 .

Option (C) is correct .

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