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I'd just go with (x + 5)^2 + (y + 7)^2 = 74 where ^2 means 'to the power of 2' or 'squared.

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

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A cord that passes through the center of a circle is a diameter of that circle. And you've probably guessed that this is the largest cord of that circle.

Neither secant nor tangent pass through the center of a circle. A secant passes through one point on the circle and the tangent passes through two points on a circle.

A chord that passes through the center of a circle is its diameter.

diameter

A secant is a line that passes through a point on the circle and the center of the circle. It intersects the circle at two different points.

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A diameter is a segment that passes through the center of a circle and has both endpoints on the circle.

A cord that passes through the center of a circle is a diameter of that circle. And you've probably guessed that this is the largest cord of that circle.

The secant of a circle passes through the center of a circle sometimes

Neither secant nor tangent pass through the center of a circle. A secant passes through one point on the circle and the tangent passes through two points on a circle.

yes a diameter passes through the center of a circle

A chord that passes through the center of a circle is its diameter.

The equation of a circle with center (0,2) and radius r is x^2+(y-2)^2=r^2 Since it passes through (0,0) (the origin) 0^2+(0-2)^2=r^2 r^2=4 The equation of the circle is x^2+(y-2)^2=4

It is the diameter of the circle.

diameter

A secant is a line that passes through a point on the circle and the center of the circle. It intersects the circle at two different points.

(x-5)2 + y2 = 17