Question

X^2+y^2-4x=11 найти центр окружности

Answer 1

Ответ:

решение смотри на фотографии

Answer 2

Finding the Center of a Circle

To find the center of a circle given the equation x^2 + y^2 - 4x = 11, we can rewrite the equation in the standard form of a circle equation, which is (x - h)^2 + (y - k)^2 = r^2. In this form, the coordinates of the center of the circle are (h, k), and the radius of the circle is r.

To rewrite the equation in standard form, we need to complete the square for both the x and y terms. Let's go through the steps:

1. Move the constant term to the right side of the equation: x^2 + y^2 - 4x = 11 becomes x^2 - 4x + y^2 = 11

2. Complete the square for the x terms: To complete the square for the x terms, we need to take half of the coefficient of x, square it, and add it to both sides of the equation. The coefficient of x is -4, so half of it is -2. Squaring -2 gives us 4. Adding 4 to both sides of the equation, we get: x^2 - 4x + 4 + y^2 = 11 + 4 Simplifying, we have: (x - 2)^2 + y^2 = 15

Now we have the equation in standard form, where the center of the circle is (2, 0) and the radius is the square root of 15.

Therefore, the center of the circle is (2, 0).