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Endpoints of Diameter: (-5,-8) and (7,2) Standard Form:

Endpoints of Diameter: (−5,−8) (-5,-8) and (7,2) (7,2) \newlineStandard Form:

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Full solution

Q. Endpoints of Diameter: (−5,−8) (-5,-8) and (7,2) (7,2) \newlineStandard Form:
  1. Find Midpoint Formula: To find the center of the circle, we need to find the midpoint of the diameter. The midpoint formula is ((x1+x2)/2,(y1+y2)/2)((x_1 + x_2)/2, (y_1 + y_2)/2).
  2. Plug in Endpoints: Using the endpoints (−5,−8)(-5,-8) and (7,2)(7,2), we plug them into the midpoint formula: igg( rac{-5 + 7}{2}, rac{-8 + 2}{2}igg).
  3. Calculate Midpoint: Calculating the midpoint gives us (22,−62)(\frac{2}{2}, \frac{-6}{2}), which simplifies to (1,−3)(1, -3).
  4. Find Center: The center of the circle is at (1,−3)(1, -3).

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