Draw up the equation of the circle, if it is known that it passes through the origin of coordinates

Draw up the equation of the circle, if it is known that it passes through the origin of coordinates, and its center coincides with the point C (1; -4).

The elimination of the circle has the form:

(x – x0) ^ 2 + (y – y0) ^ 2 = R ^ 2, where:

(x0; y0) – coordinates of the center of the circle.

R is the radius.

We know the coordinates of the center of the circle, find the radius.

In our case, the radius will be equal to the length of the segment between point C (1; -4) and the origin (0; 0).

OC ^ 2 = (1 – 0) ^ 2 + (-4 – 0) ^ 2;

OC ^ 2 = 1 + 16 = 17.

We will not extract the square root of the number 17 due to lack of need.

OC = R, then OC ^ 2 = R ^ 2.

The equation of the circle is:

(x – 1) ^ 2 + (y + 4) ^ 2 = 17.