Write the equation of a circle passing through point A (1; 3), if it is known that the center

Write the equation of a circle passing through point A (1; 3), if it is known that the center of the circle lies on the abscissa axis, and the radius is 5. How many such circles exist?

We have a point belonging to the circle: A (1; 3).

The radius of the circle and the coordinates of the center of the circle are known – they have the form (x0; 0).

Let’s write the equation of the circle:

(x – x0) ^ 2 + (y – y0) ^ 2 = R ^ 2.

We substitute the values we know:

(1 – x0) ^ 2 + (3 – 0) ^ 2 = 25;

(1 – x0) ^ 2 + 9 = 25;

(1 – x0) ^ 2 = 16;

1) 1 – x0 = -4;

x0 = 5;

2) 1 – x0 = 4;

x0 = -3.

We got two circles, since we also have two pairs of coordinates for the center of the circle – (5; 0) and (-3; 0).