Write the equation in standard form for the circle x2+y2+2x–16=0.Submit

The given equation is x^2 + y^2 + 2x - 16 = 0.

To write this equation in standard form for a circle, we need to complete the square for the x-terms.

The standard form for the equation of a circle is (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius.

Step 1: Rearrange the equation to group the x-terms together: (x^2 + 2x) + y^2 = 16.

Step 2: Complete the square for the x-terms. To do this, take half of the coefficient of x, square it, and add it to both sides of the equation. Half of 2 is 1, and 1^2 = 1, so we get: (x^2 + 2x + 1) + y^2 = 16 + 1.

Step 3: Simplify the equation to get it in standard form: (x + 1)^2 + y^2 = 17.

So, the equation of the circle in standard form is (x + 1)^2 + y^2 = 17. The center of the circle is at (-1, 0) and the radius is √17.