Question

If a circle has a diameter with endpoints of (-3, 0) and (5, 4) then the equation of the circle is?

Answer 1

Answer:

(x - 1)² + (y - 2)² = 20

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

Given the endpoints, then the centre is at the midpoint

C = [ $\frac{-3+5}{2}$, $\frac{0+4}{2}$ ] = (1, 2 )

The radius is the distance from the centre to either of the 2 endpoints.

Use the distance formula to find r

r = $\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }$

with (x₁, y₁ ) = (1, 2) and (x₂, y₂ )= (- 3, 0)

r = $\sqrt{(-3-1)^2+(0-2)^2}$

  = $\sqrt{(-4)^2+(-2)^2}$

  = $\sqrt{16+4}$

  = $\sqrt{20}$

Thus equation of circle is

(x - 1)² + (y - 2)² = ($\sqrt{20}$ )² , that is

(x - 1)² + (y - 2)² = 20