Question

1. Складіть рівняння кола з центром у точці М (0; -3), якщо воно проходить через точку К (-2; 3).

Answer 1

1. Складіть рівняння кола з центром у точці М (0; -3), якщо воно проходить через точку К (-2; 3).

Находим радиус окружности.

R = √((-2-0)² + (3-(-3)) = √(4 + 36) = √40 = 2√10.

Уравнение: x² + (y + 3)² = (2√10)² или x² + (y + 3)² = 40.

Answer 2

Equation of a Circle with Center at Point M(0, -3) and Passing through Point K(-2, 3)

To find the equation of a circle with a center at point M(0, -3) and passing through point K(-2, 3), we can use the general equation of a circle:

Equation of a Circle: (x - h)^2 + (y - k)^2 = r^2

Where: - (h, k) represents the coordinates of the center of the circle. - r represents the radius of the circle.

In this case, the center of the circle is at point M(0, -3), so the values of h and k are 0 and -3, respectively.

To find the radius of the circle, we can use the distance formula between the center point M(0, -3) and the point K(-2, 3):

Distance Formula: d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Substituting the values of the points M(0, -3) and K(-2, 3) into the distance formula:

d = sqrt((-2 - 0)^2 + (3 - (-3))^2) = sqrt((-2)^2 + (3 + 3)^2) = sqrt(4 + 36) = sqrt(40) = 2 * sqrt(10)

Therefore, the radius of the circle is 2 * sqrt(10).

Substituting the values of h, k, and r into the equation of a circle:

(x - 0)^2 + (y - (-3))^2 = (2 * sqrt(10))^2 x^2 + (y + 3)^2 = 40

Hence, the equation of the circle with a center at point M(0, -3) and passing through point K(-2, 3) is x^2 + (y + 3)^2 = 40.

Please let me know if you need any further assistance!