Question

homework assignment 8.0 circles
score: 6/7 answered: 6/7
question 7
draw a circle with an equation of $x^{2}-4x + y^{2}-2y = 4$.
clear all draw:
question help: video 1 video 2 written example 1

Explanation:

Step1: Complete the square for x-terms

For \(x^2 - 4x\), take half of -4, which is -2, square it: \((-2)^2 = 4\). Add 4 to both sides.
\(x^2 - 4x + 4 + y^2 - 2y = 4 + 4\)

Step2: Complete the square for y-terms

For \(y^2 - 2y\), take half of -2, which is -1, square it: \((-1)^2 = 1\). Add 1 to both sides.
\(x^2 - 4x + 4 + y^2 - 2y + 1 = 4 + 4 + 1\)

Step3: Rewrite as perfect squares

\((x - 2)^2 + (y - 1)^2 = 9\)

Step4: Identify center and radius

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, center is \((2, 1)\) and radius \(r = \sqrt{9} = 3\).

Answer:

To draw the circle:

• Center: Plot the point \((2, 1)\) on the coordinate grid.
• Radius: From the center \((2, 1)\), move 3 units up, down, left, and right (e.g., to \((2, 4)\), \((2, -2)\), \((-1, 1)\), \((5, 1)\)) and draw a circle passing through these points.