Question

Запиши рiвняння кола iз центром у точці 0(-10; 3) та діаметром 6 см​

Answer 1

Уравнение окружности имеет вид (х-а)²+(у-в)²=R², где т.О(а; в) - центр окружности; R - радиус. Решаем. D=2R, значит R=D:2=6:2=3. Значит, (х-(-10))²+(у-3)²=3²; (х+10)²+(у-3)²=9.

Answer 2

Equation of a Circle with Center at (0, -10; 3) and Diameter of 6 cm

To write the equation of a circle with a center at the point (0, -10; 3) and a diameter of 6 cm, we can use the standard form of the 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 (0, -10; 3), which means h = 0 and k = -10; 3. The diameter of the circle is given as 6 cm, which means the radius (r) is half of the diameter, i.e., r = 6 cm / 2 = 3 cm.

Substituting the values into the equation, we get:

Equation of the Circle: (x - 0)^2 + (y - (-10; 3))^2 = 3^2

Simplifying further:

Equation of the Circle: x^2 + (y + 10; 3)^2 = 9

Therefore, the equation of the circle with a center at (0, -10; 3) and a diameter of 6 cm is x^2 + (y + 10; 3)^2 = 9.

Please note that the equation is in standard form and represents a circle with a radius of 3 cm and a center at (0, -10; 3).

I hope this helps! Let me know if you have any further questions.