Write the equation in standard form for the circle x2+y2–14x=–48.

The equation of a circle in standard form is (x-h)² + (y-k)² = r², where (h,k) is the center of the circle and r is the radius.

The given equation is x² + y² - 14x = -48.

To convert this into standard form, we need to complete the square for the x terms.

First, rearrange the equation to group the x terms together:

x² - 14x + y² = -48

Next, take half of the coefficient of x, square it, and add it to both sides of the equation. Half of -14 is -7, and (-7)² = 49.

x² - 14x + 49 + y² = -48 + 49

This simplifies to:

(x - 7)² + y² = 1

So, the equation of the circle in standard form is (x - 7)² + y² = 1. The center of the circle is at (7, 0) and the radius is 1.