Question

Which of the following is the equation for a circle with a diameter that has endpoints at (2, 10) and (10,6)?

A.(x + 6)2 + (y + 8)2 = 80
B.(x - 6)2 + (y - 3)2 = 80
C.(x + 6)2 + (y + 8)2 = 20
D(x - 6)2 + (y - 3)2 = 20

Answer 1

• (x - 6)² + (y - 8)² = 20

Explanation:

Find the center, the midpoint of the ends of the diameter.

Use midpoint formula for each coordinate:

• x = (2 + 10) / 2 = 12/2 = 6
• y = (10 + 6) / 2 = 16/2 = 8

Find the square of the radius using distance formula between points:

• (2, 10) and (6, 8)

• 
  `r^2=(x_2-x_1)^2+(y_2-y_1)^2`
• 
  `r^2=(6-2)^2+(8-10)^2`
• 
  `r^2=4^2+(-2)^2=16+4 = 20`

Use the equation of circle:

• (x - h)² + (y - k)² = r²

We know that (h, k) is the center (6, 8), substitute into above equation:

• (x - 6)² + (y - 8)² = 20