# Find the equation of the circle having the endpoints of the diameter (4 ,6) and (0, -2)

1
by liezel9

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by liezel9

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Given: (4,6) and 0,-2)

1) Find the center (h, k) using midpoint formula.

Midpoint =

x₁ = 4 x₂ = 0

y₁ = 6 y₂ = -2

Midpoint (Center) =

= (⁴/₂, ⁴/₂)

= (2, 2)

2) Find the distance of the radius by solving for the distance of the two endpoints of diameter divided by 2. (Radius is 1/2 of diameter of the circle.)

Radius = /2

Radius =

Radius =

Radius =

Radius = (1/2)(4)

Radius =

3) Equation:

Standard or Center-Radius Form:

(x - h)² + (y-h)² = r²

(x - 2)² + (y - 2)² = (

(x-2)² + (y-2)² = (4)(5)

4.) Equation of the circle in general form, x² + y² + Cx + Dy + E = 0:

(x-2)² + (y-2)² = 20

x² - 4x + 4 + y² - 4y + 4 - 20 = 0