# What will be the equation of the circle with a center at (–4, 9) and a diameter of 10 units?

**Solution:**

We can make use of the standard form of the equation of the circle. Go through the step-by-step procedure to get the final equation of the circle.

Given, center coordinates = (-4, 9) and diameter = 10 units.

radius = diameter / 2 = 5 units

Using the standard equation of the circle, which 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.

Thus on substituting the value of h, k, and r in the standard equation, we get:

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

⇒^{ }(x + 4)^{2} + (y - 9)^{2} = 25

Thus the equation of the circle, can be given as ^{ }(x + 4)^{2} + (y - 9)^{2} = 25.

⇒ x^{2} +y^{2} +8x-18y = 25 -16 -81

⇒ x^{2} +y^{2} +8x-18y =-72

## What will be the equation of the circle with a center at (–4, 9) and a diameter of 10 units?

**Summary:**

The equation of the circle, can be given as ^{ }(x + 4)^{2} + (y - 9)^{2} = 25 or x^{2} +y^{2} +8x-18y =-72

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