Find the coordinates of the intersection points of the circle x ^ 2 + y ^ 2 – 10x – 6y +9 = 0. with abscissa axis

In order to find the coordinates of the points of intersection of the circle x ^ 2 + y ^ 2 – 10x – 6y + 9 = 0 with the abscissa axis, it is necessary to substitute the value y = 0 into the equation of the circle and solve the resulting equation of the relative variable x.

Substituting the value y = 0 into the equation, we get:

x ^ 2 + 0 ^ 2 – 10x – 6 * 0 + 9 = 0.

We solve the resulting equation:

x ^ 2 – 10x + 9 = 0;

x = 5 ± √ (25 – 9) = 5 ± √16 = 5 ± 4;

x1 = 5 – 4 = 1;

x = 5 + 4 = 9.

Consequently, this circle intersects the abscissa at points (1; 0) and (9; 0).

Answer: (1; 0) and (9; 0).