Question

X^2+y^2=14y-2x-50 решите пж​

Answer 1

Смотри..........................

Answer 2

To solve the equation $x^2 + y^2 = 14y - 2x - 50$, we need to manipulate the equation and try to express one variable in terms of the other. Let's start by completing the square for both $x$ and $y$.

Step 1: Complete the square for $x$:

$$x^2 + 2x = x^2 + 2x + 1 - 1 = (x + 1)^2 - 1.$$

Step 2: Rewrite the equation with the completed square for $x$:

$$(x + 1)^2 + y^2 = 14y - 51.$$

Step 3: Move the constant term to the right side:

$$(x + 1)^2 + y^2 = 14y + 51.$$

Step 4: Complete the square for $y$:

$$y^2 - 14y = y^2 - 14y + 49 - 49 = (y - 7)^2 - 49.$$

Step 5: Rewrite the equation with the completed square for $y$:

$$(x + 1)^2 + (y - 7)^2 = 49.$$

The equation now has the form of a circle with center $(-1, 7)$ and radius $r = \sqrt{49} = 7$.

So, the solution to the equation is the circle centered at $(-1, 7)$ with radius $7$.