Ver en españolWrite the equation in standard form for the circle x2+y2=10y–24.Submit

The given equation is x^2 + y^2 = 10y - 24.

To write the equation in standard form for the circle, we need to complete the square for the y terms.

First, let's rearrange the equation to group the y terms together:

x^2 + y^2 - 10y = -24

Next, we need to complete the square for the y terms. To do this, we take half of the coefficient of y, square it, and add it to both sides of the equation. Half of -10 is -5, and (-5)^2 = 25.

x^2 + y^2 - 10y + 25 = -24 + 25

Simplify the right side:

x^2 + y^2 - 10y + 25 = 1

Now, we can rewrite the left side of the equation as a binomial squared:

x^2 + (y - 5)^2 = 1

This is the standard form of the equation for the circle.