Question

Точка Q - центр кола, QA - радіус кола. Складіть рівняння кола, якщо Q (0;4), A (5;16).​

Answer 1

Ответ:

решение смотри на фотографии

Answer 2

Equation of a Circle

To find the equation of a circle, we need the coordinates of its center and the radius. In this case, the center of the circle is given as point Q(0, 4) and point A(5, 16) lies on the circle.

The formula for the equation of a circle is:

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

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

Let's calculate the radius first using the distance formula between points Q and A:

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

Substituting the coordinates of Q(0, 4) and A(5, 16):

Radius (r) = √((5 - 0)^2 + (16 - 4)^2) = √(5^2 + 12^2) = √(25 + 144) = √169 = 13

Now, we can substitute the values of the center (h, k) and the radius (r) into the equation of a circle:

`(x - 0)^2 + (y - 4)^2 = 13^2`

Simplifying further:

`x^2 + (y - 4)^2 = 169`

Therefore, the equation of the circle with center Q(0, 4) and radius QA = 13 is `x^2 + (y - 4)^2 = 169`.

Please note that the equation of a circle can also be written in standard form as `x^2 + y^2 + Dx + Ey + F = 0`, where D, E, and F are constants. However, in this case, we have used the general form of the equation.

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