# How do you write the equation of the circle with endpoints of its diameter at (-4,7) and (8,-9)?

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The equation of the circle with endpoints of its diameter at (-4,7) and (8,-9) can be written as:

[(x - h)^2 + (y - k)^2 = r^2]

where ((h, k)) is the center of the circle and (r) is the radius. To find the center, use the midpoint formula:

[h = \frac{x_1 + x_2}{2}] [k = \frac{y_1 + y_2}{2}]

Plugging in the values:

[h = \frac{-4 + 8}{2} = 2] [k = \frac{7 - 9}{2} = -1]

Next, calculate the radius using the distance formula:

[r = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}]

Plugging in the values:

[r = \sqrt{(8 - (-4))^2 + (-9 - 7)^2}] [r = \sqrt{12^2 + (-16)^2}] [r = \sqrt{144 + 256}] [r = \sqrt{400}] [r = 20]

Therefore, the equation of the circle is:

[(x - 2)^2 + (y + 1)^2 = 20^2]

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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