Has a diameter with endpoints A(-3,2) and B(7,4)

Question

With graph 

Answer 1

Hi, for the equation of a circle you first need to find the center;

 

midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2)

 = (-3 + 7)/2, (2 + 4)/2)

  = (2, 3)

Now that we have the center, we need the radius:

 

r = √(x1 - x2)² + (y1 - y2)²

Let's use (2,3) for (x1,y1) and (7,4) for (x2,y2)

r = √(7-2)² + (4-3)²

r = √25 + 1

r = √26 

Now we can find the equation of circle with center (2,3) and radius √26 

 

(x - 2)² + (y - 3)² = 26