# Which equation represents a circle with a center at (-4, 9) and a diameter of 10 units?

(x - 9)2 + (y + 4)^{2} = 25

(x + 4)2 + (y - 9)^{2} = 25

(x - 9)2 + (y + 4)^{2} = 100

(x + 4)2 + (y - 9)^{2} = 100

**Solution:**

Given: Center of the circle(-4,9) and

Diameter = 10 units

Radius = diameter/2 = 10/2 = 5 units

The standard equation of the circle is

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

Where h = x coordinate of the center

k = y coordinate of the center

r = radius of the circle

Now substituting the values in the equation

(x + 4)^{2} + (y - 9)^{2} = 5^{2}

(x + 4)^{2} + (y - 9)^{2} = 25

Therefore, the equation of the circle is (x + 4)^{2} + (y - 9)^{2} = 25.

## Which equation represents a circle with a center at (–4, 9) and a diameter of 10 units?

(x - 9)^{2} + (y + 4)^{2} = 25

(x + 4)^{2} + (y - 9)^{2} = 25

(x - 9)^{2} + (y + 4)^{2} = 100

(x + 4)^{2} + (y - 9)^{2} = 100

**Summary:**

The equation which represents a circle with a center at (-4, 9) and a diameter of 10 units is (x + 4)^{2} + (y - 9)^{2} = 25.

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