Equation of A Circle?

Question

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Or Use this Information:

Circle Hits Points

(0,-2)(2,0)(0,2)(-2,0)

Center is Origin(0,0)

Which equation is shown by the graph in Figure 2?

a. 2x2 + 2y2 = 2

b. (x - 2)2 + (y - 2)2 = 4

c. x2 + y2 = 2

d. 3x2 + 3y2 = 12

Answer 1

General form is

(x - h)^2 + (y - k)^2 = r^2

where r = radius

(h, k) = center

So....

Since this circle is centered at the radius and hits the point (0, 2), we know the radius is 2 units.

(x - 0)^2 + (y - 0)^2 = 2^2

x^2 + y^2 = 4

Which is not one of the options you have listed.  (Does C have a typo??)

Answer 2

if the center of the circle is at (0,0), then the other points you mention indicate that the circle has a radius of 2

the equation for a circle can be written as:

(x-a)^2 +(y-b)^2 = r^2

where r is the radius of the circle, and (a,b) are the coordinates of the center of the circle

here, a=0 and b=0, and r=2, so the equation is:

x^2+y^2=4