Question

Give the equation of the circle centered at the origin and passing through the point (0,-2).

Answer 1

Apply:

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

Where (h,k) is the center of the circle, and r= radius.

Since the center is on (0,0) , h=0 and k=0

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

Since it passes through the point (0,-2) = (x,y)

$(0)^2+(-2)^2=r^2$

Solve for r^2

$4=r^2^{}$

The final equation is:

$x^2+y^2=4$