Question

complete the square and write the given equation in standard form. then give the center and radius of the circle and graph the equation. x² + y² + 4x - 2y - 31 = 0 the equation of the circle in standard form is (x + 2)² + (y - 1)² = 36 (simplify your answer.) the center of the circle is □. (type an ordered pair.)

Explanation:

Step1: Recall the standard form of a circle equation

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

Step2: Identify \(h\) and \(k\) from the given standard form \((x + 2)^{2}+(y - 1)^{2}=36\)

Compare \((x + 2)^{2}+(y - 1)^{2}=36\) with \((x - h)^{2}+(y - k)^{2}=r^{2}\).
For the \(x\) - part: \((x+2)=(x - (- 2))\), so \(h=-2\).
For the \(y\) - part: \((y - 1)\), so \(k = 1\).

Answer:

The center of the circle is \((-2,1)\)