Question

17.1.1 equation of a circle
equation. graph the circle.
a. ((x + 3)^2 + (y - 2)^2 = 9)
b. ((x + 4)^2 + (y - 8)^2 = 36)
open - ended question
explain how you would graph b. on the coordinate plane.
type your answer here
rewatch

Explanation:

Step1: Identify Circle Equation Form

The standard circle equation is \((x - h)^2 + (y - k)^2 = r^2\), where \((h, k)\) is the center and \(r\) is the radius. For \((x + 4)^2 + (y - 8)^2 = 36\), rewrite \(x + 4\) as \(x - (-4)\) and \(36\) as \(6^2\). So, \(h = -4\), \(k = 8\), \(r = 6\).

Step2: Plot the Center

Locate the center \((-4, 8)\) on the coordinate plane. Move 4 units left of the origin on the x - axis and 8 units up on the y - axis.

Step3: Draw the Circle

Using the radius \(r = 6\), draw a circle centered at \((-4, 8)\). The radius means the distance from the center to any point on the circle is 6 units. So, from \((-4, 8)\), move 6 units left/right (x - direction: \(-4\pm6\)) and 6 units up/down (y - direction: \(8\pm6\)) to mark points on the circle, then sketch the circle through these points.

Answer:

To graph \((x + 4)^2+(y - 8)^2 = 36\):

1. Identify Center and Radius: From the standard circle equation \((x - h)^2+(y - k)^2 = r^2\), here \(h=-4\), \(k = 8\) (center: \((-4,8)\)), and \(r=\sqrt{36}=6\).
2. Plot the Center: On the coordinate plane, find \((-4,8)\) (4 units left of the origin on the x - axis, 8 units up on the y - axis).
3. Draw the Circle: Using a compass or by plotting points 6 units from the center (e.g., \((-4 + 6,8)=(2,8)\), \((-4 - 6,8)=(-10,8)\), \((-4,8 + 6)=(-4,14)\), \((-4,8 - 6)=(-4,2)\)), then sketch the circle through these points.