Answer :
Sure, let's break down the steps to draw the circle given by the equation [tex]\((x+2)^2+(y+3)^2=1\)[/tex].
### Understanding the Equation
This is the equation of a circle in the standard form [tex]\((x-h)^2 + (y-k)^2 = r^2\)[/tex], where:
- [tex]\((h, k)\)[/tex] is the center of the circle.
- [tex]\(r\)[/tex] is the radius of the circle.
For the given equation [tex]\((x+2)^2 + (y+3)^2 = 1\)[/tex]:
- The center [tex]\((h, k)\)[/tex] is [tex]\((-2, -3)\)[/tex].
- The radius [tex]\(r\)[/tex] is [tex]\(\sqrt{1} = 1\)[/tex].
### Drawing the Circle
1. Plot the Center: Mark the center of the circle at the coordinates [tex]\((-2, -3)\)[/tex].
2. Draw the Radius:
- From the center, measure a distance of 1 unit in all directions (up, down, left, and right). This will help in outlining the circumference of the circle.
3. Outline the Circle:
- Using the center as the reference point, draw a smooth curve that maintains a constant distance (1 unit) from the center. You can use a compass or freehand if you're drawing manually on paper, or use graphing software for precision.
### Adding Details
- Axes: Draw the x-axis and y-axis for reference. Ensure the center [tex]\((-2, -3)\)[/tex] is accurately placed relative to these axes.
- Label the Circle: You can add a title or label to your circle to specify that it represents the equation [tex]\((x+2)^2 + (y+3)^2 = 1\)[/tex].
- Grid: A grid can help ensure precision and make it easier to draw the circle accurately.
Here is a conceptual representation of the circle:
```
y-axis
|
-3 (center)
|
|
|
|
|
| (edge at 1 unit)
-------+----------------------- x-axis
-3 -2 -1 x
```
In the grid above:
- The center of the circle is [tex]\((-2, -3)\)[/tex].
- Points such as [tex]\((-2, -2)\)[/tex], [tex]\((-2, -4)\)[/tex], [tex]\((-1, -3)\)[/tex], and [tex]\((-3, -3)\)[/tex] should each lie 1 unit from the center, showing the circle's radius accurately.
By following these steps, you'll be able to draw the circle [tex]\((x+2)^2+(y+3)^2=1\)[/tex] accurately.
### Understanding the Equation
This is the equation of a circle in the standard form [tex]\((x-h)^2 + (y-k)^2 = r^2\)[/tex], where:
- [tex]\((h, k)\)[/tex] is the center of the circle.
- [tex]\(r\)[/tex] is the radius of the circle.
For the given equation [tex]\((x+2)^2 + (y+3)^2 = 1\)[/tex]:
- The center [tex]\((h, k)\)[/tex] is [tex]\((-2, -3)\)[/tex].
- The radius [tex]\(r\)[/tex] is [tex]\(\sqrt{1} = 1\)[/tex].
### Drawing the Circle
1. Plot the Center: Mark the center of the circle at the coordinates [tex]\((-2, -3)\)[/tex].
2. Draw the Radius:
- From the center, measure a distance of 1 unit in all directions (up, down, left, and right). This will help in outlining the circumference of the circle.
3. Outline the Circle:
- Using the center as the reference point, draw a smooth curve that maintains a constant distance (1 unit) from the center. You can use a compass or freehand if you're drawing manually on paper, or use graphing software for precision.
### Adding Details
- Axes: Draw the x-axis and y-axis for reference. Ensure the center [tex]\((-2, -3)\)[/tex] is accurately placed relative to these axes.
- Label the Circle: You can add a title or label to your circle to specify that it represents the equation [tex]\((x+2)^2 + (y+3)^2 = 1\)[/tex].
- Grid: A grid can help ensure precision and make it easier to draw the circle accurately.
Here is a conceptual representation of the circle:
```
y-axis
|
-3 (center)
|
|
|
|
|
| (edge at 1 unit)
-------+----------------------- x-axis
-3 -2 -1 x
```
In the grid above:
- The center of the circle is [tex]\((-2, -3)\)[/tex].
- Points such as [tex]\((-2, -2)\)[/tex], [tex]\((-2, -4)\)[/tex], [tex]\((-1, -3)\)[/tex], and [tex]\((-3, -3)\)[/tex] should each lie 1 unit from the center, showing the circle's radius accurately.
By following these steps, you'll be able to draw the circle [tex]\((x+2)^2+(y+3)^2=1\)[/tex] accurately.
