Points A (4; -1), B (2; -4), C (0; -1) are the vertices of the triangle ABC.

Points A (4; -1), B (2; -4), C (0; -1) are the vertices of the triangle ABC. Make an equation of a circle with a center at point B and passing through point A. Does it belong to circle C.

The equation of a circle having a center at point B with coordinates (2; – 4), radius R, has the form: (x – 2) ^ 2 + (y – (- 4)) ^ 2 = R ^ 2. By condition, A (4; – 1) is the point of the circle, B (2; – 4) is the center of the circle, so you can find the radius of the circle by the formula for the length of the segment: R ^ 2 = AB ^ 2 = (2 – 4) ^ 2 + (- 4 – (- 1)) ^ 2; R ^ 2 = 13. Now you can finally compose the equation of the circle: (x – 2) ^ 2 + (y + 4) ^ 2 = 13. To check whether the point C (0; – 1) belongs to the circle, you need to substitute into the equation circle of the coordinate value of this point. If you get a true numerical equality, then the point belongs to the circle, if not, then it does not belong: (0 – 2) ^ 2 + (- 1 + 4) ^ 2 = 13; 13 = 13.
Answer: the equation of the circle is (x – 2) ^ 2 + (y + 4) ^ 2 = 13, point C belongs to this circle.