This equation represents a circle. To rewrite the equation in standard form, we complete the square for both the x and y terms:
(x^2 + 4x) + (y^2 - 10y) = -29
To complete the square for the x term, we take half of the coefficient of x, square it, then add and subtract it inside the parentheses:
(x^2 + 4x + 4) + (y^2 - 10y) = -29 + 4(x + 2)^2 + (y^2 - 10y) = -25
To complete the square for the y term, we take half of the coefficient of y, square it, then add and subtract it inside the parentheses:
(x + 2)^2 + (y^2 - 10y + 25) = -25 + 25(x + 2)^2 + (y - 5)^2 = 0
Now, the equation is in standard form:
(x + 2)^2 + (y - 5)^2 = 0
Since the right side of the equation is equal to 0, this represents a circle with center at (-2, 5) and radius of 0, meaning it is just a single point.
This equation represents a circle. To rewrite the equation in standard form, we complete the square for both the x and y terms:
(x^2 + 4x) + (y^2 - 10y) = -29
To complete the square for the x term, we take half of the coefficient of x, square it, then add and subtract it inside the parentheses:
(x^2 + 4x + 4) + (y^2 - 10y) = -29 + 4
(x + 2)^2 + (y^2 - 10y) = -25
To complete the square for the y term, we take half of the coefficient of y, square it, then add and subtract it inside the parentheses:
(x + 2)^2 + (y^2 - 10y + 25) = -25 + 25
(x + 2)^2 + (y - 5)^2 = 0
Now, the equation is in standard form:
(x + 2)^2 + (y - 5)^2 = 0
Since the right side of the equation is equal to 0, this represents a circle with center at (-2, 5) and radius of 0, meaning it is just a single point.