Question

Which is the standard equation of a circle with diameter with A(0, -1) and B(2, 1)?

Answer 1

The standart equation:

(x - xc)² + (y - yc)² = r²

For this case, we have the diameter given by 2 points, A and B, the center will be the middle point of this line. We can get the middle point of this line adding both x's and dividing by two, the same for y.

M = (0+2/2, -1+1/2)

M = (2/2, 0/2)

M = (1, 0)

For the radius we need to know the distance between the middle point and A or B,

d = $\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

Let's use B.

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

d=$\sqrt{(-1)^2+(-1)^2}$

d=$\sqrt{1+1}$

d=$\sqrt{2}$

Knowing the radius we can put all in the formule

(x - xc)² + (y - yc)² = r²

(x - 1)² + (y - 0)² = $\sqrt{2}^2$

(x - 1)² + y² = 2