Question

Скласти рівняння кола центр якого – точка О (-3;1) і проходить через точку А( 2;0)

Answer 1

Ответ:

((x + 3)^2 + (y - 1)^2 = 5^2).

Answer 2

Equation of a Circle

To find the equation of a circle with center O(-3, 1) that passes through point A(2, 0), we can use the general equation of a circle:

(x - h)^2 + (y - k)^2 = r^2

where (h, k) represents the center of the circle and r represents the radius.

In this case, the center of the circle is O(-3, 1), so h = -3 and k = 1. The circle also passes through point A(2, 0).

To find the radius, we can use the distance formula between the center of the circle and point A:

r = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Substituting the coordinates of O(-3, 1) and A(2, 0) into the formula, we get:

r = sqrt((2 - (-3))^2 + (0 - 1)^2) = sqrt(25 + 1) = sqrt(26)

Therefore, the equation of the circle is:

(x + 3)^2 + (y - 1)^2 = 26

Please let me know if there's anything else I can help you with!