Give the equation of a circle with a diameter that has endpoints (10,-8) and (-6,0).

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Give the equation of a circle with a diameter that has endpoints  (10,-8) and  (-6,0).

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Calculate Midpoint: To find the equation of a circle, we need the center and the radius. The center of the circle is the midpoint of the diameter. Let's calculate the midpoint of the diameter with endpoints (10,-8) and (-6,0). Midpoint formula: $ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) $ $ M = \left( \frac{10 + (-6)}{2}, \frac{-8 + 0}{2} \right) $ $ M = \left( \frac{4}{2}, \frac{-8}{2} \right) $ $ M = (2, -4) $Find Radius: Now that we have the center of the circle, we need to find the radius. The radius is half the length of the diameter. We can calculate the length of the diameter using the distance formula and then divide by 2 to get the radius. Distance formula: $ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $ $ d = \sqrt{(-6 - 10)^2 + (0 - (-8))^2} $ $ d = \sqrt{(-16)^2 + (8)^2} $ $ d = \sqrt{256 + 64} $ $ d = \sqrt{320} $ Radius $ r = \frac{d}{2} = \frac{\sqrt{320}}{2} $Simplify Radius: We can simplify the expression for the radius by factoring out perfect squares from under the radical. $ \sqrt{320} = \sqrt{64 \cdot 5} $ $ \sqrt{320} = \sqrt{64} \cdot \sqrt{5} $ $ \sqrt{320} = 8\sqrt{5} $ So the radius $ r = \frac{8\sqrt{5}}{2} = 4\sqrt{5} $Write Circle Equation: With the center (2, -4) and the radius $ 4\sqrt{5} $, we can write the equation of the circle in the standard form: $ (x - h)^2 + (y - k)^2 = r^2 $, where (h, k) is the center and r is the radius. $ (x - 2)^2 + (y + 4)^2 = (4\sqrt{5})^2 $ $ (x - 2)^2 + (y + 4)^2 = 16 \cdot 5 $ $ (x - 2)^2 + (y + 4)^2 = 80 $

Give the equation of a circle with a diameter that has endpoints $(10,-8)$ and $(-6,0)$ .

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Give the equation of a circle with a diameter that has endpoints (10,−8) (10,-8) (10,−8) and (−6,0) (-6,0) (−6,0).

Give the equation of a circle with a diameter that has endpoints $(10,-8)$ and $(-6,0)$ .