Question

Складіть рівняння кола, яке проходить через точкуK(0; -5) і має центр в точці O(1; -3)​

Answer 1

Equation of a Circle

To find the equation of a circle that passes through the point K(0, -5) and has its center at the point O(1, -3), we can use the general equation of a circle:

Equation of a Circle: The equation of a circle with center (h, k) and radius r is given by: (x - h)^2 + (y - k)^2 = r^2

In this case, the center of the circle is O(1, -3), so the equation becomes: (x - 1)^2 + (y + 3)^2 = r^2

To find the radius r, we need to use the fact that the circle passes through the point K(0, -5). Substituting the coordinates of K into the equation, we get: (0 - 1)^2 + (-5 + 3)^2 = r^2 (-1)^2 + (-2)^2 = r^2 1 + 4 = r^2 5 = r^2

Therefore, the equation of the circle that passes through the point K(0, -5) and has its center at the point O(1, -3) is: (x - 1)^2 + (y + 3)^2 = 5

Please let me know if you need any further assistance!