Write the equation of a circle centered at point B (4; 0) if it passes through point A (7; 4).

The general equation of the circle is: (x – a) ^ 2 + (y – b) ^ 2 = R ^ 2, where a and b are the coordinates of the center of the circle, R is its radius.

From the condition of the task it is seen that a = 4 and b = 0.

Find the radius of the circle – the distance between the center of the circle (point B) and point A of the circle. More precisely, for the equation of a circle you need a square of the radius:

R2 = (x2 -x1) ^ 2 + (y2 – y1) ^ 2, A (x1; y1) and B (x2; y2).

R ^ 2 = (7 – 4) ^ 2 + (4 – 0) ^ 2.

R ^ 2 = 3 ^ 2 + 4 ^ 2.

R ^ 2 = 25.

Let’s write the equation of the circle: (x – 4) ^ 2 + (y – 0) ^ 2 = 25.

Answer: (x – 4) ^ 2 + y ^ 2 = 25.