What is the equation of the circle with its center at (0,0) that passes through (3,4).

Given that the center of the circle is the point
(0,0).

We know that the equation of the circle is given by
:

(x-a)^2 + (y-b)^2 = r^2 where (a,b) is the center and r
is the radius.

==> x^2 + y^2 =
r^2

Now we will determine the
radius.

Since the point (3,4) is on the circle, then the
distance between the point and the center is the
radius.

==> r = sqrt( 3^2 + 4^2) = sqrt25 =
5

Then, the radius of the circle is 5
units.

==> Them the equation of the circle
is:

x^2 + y^2 =
25