Question

The endpoints of the diameter of a circle are (6, 5) and (−2, 3). Which equation represents the circle?

Answer 1

Answer:

(x - 2)² + (y - 4)² = 17

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

The centre is at the midpoint of the endpoints of the diameter, that is

x = $\frac{6-2}{2}$ = $\frac{4}{2}$ = 2 and y = $\frac{5+3}{2}$ = $\frac{8}{2}$ = 4

centre = (2, 4 )

The radius is the distance from the centre to either of the endpoints

Using the distance formula to find r

r = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (2, 4) and (x₂, y₂ ) = (- 2, 3)

r = $\sqrt{(-2-2)^2+(3-4)^2}$

  = $\sqrt{(-4)^2+(-1)^2}$

  = $\sqrt{16+1}$

  = $\sqrt{17}$ ⇒ r² = 17

Thus the equation of the circle is

(x - 2)² + (y - 4)² = 17