Question

question 7
draw a circle with an equation of $x^{2}-2x + y^{2}+2y = 7$.
clear all draw:
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Explanation:

Step1: Complete the square for \(x\) terms

For \(x^{2}-2x\), we add \((\frac{-2}{2})^{2}=1\).
For \(y^{2}+2y\), we add \((\frac{2}{2})^{2} = 1\).
The equation \(x^{2}-2x + y^{2}+2y=7\) becomes \((x - 1)^{2}-1+(y + 1)^{2}-1=7\).

Step2: Simplify the equation

\((x - 1)^{2}+(y + 1)^{2}=7 + 1+1\).
So, \((x - 1)^{2}+(y + 1)^{2}=9\).

The standard form of a circle is \((x - h)^{2}+(y - k)^{2}=r^{2}\), where \((h,k)\) is the center and \(r\) is the radius.
Here, the center is \((1,-1)\) and the radius \(r = 3\).

Answer:

The circle has center \((1,-1)\) and radius \(3\). To draw it:

1. Plot the center \((1,-1)\) on the coordinate plane.
2. From the center, move \(3\) units up, down, left, and right.
3. Connect these four points to form a circle.