Answers

  • Brainly User
2016-02-03T23:59:16+08:00
Given the endpoints of the circle's diameter (2,3) and 8,7):

Steps:
1) Find the center using the midpoint formula.  
    The center is (5,5)

2) Find the radius give the center (5,5) and one of the endpoints of the diameter, (2,3) and (8,7).
    The radius is  \sqrt{13}

3) Then, write the equation of the circle given the center (5,5) and radius  \sqrt{13} .

Equation in standard-radius form:  (x-h)² + (y-k)² = r²
   
     (x-5)² + (y-5)² = ( \sqrt{13}) ^{2}
    
     (x-5)² + (y-5)² = 13   ⇒   Standard Form


Equation in general form: Ax² + By² + Cx + Dy + E = 0
   
   x² - 10x + 25 + y² -10x + 25 - 13 = 0
   
   x² + y² -10x - 10y + 25 + 25 - 13 = 0
   
   x² + y² -10x - 10y - 37 = 0  ⇒   General Form

CLICK image below to view the solution for center and radius.

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