Write the standard form of the equation of the circle having the given radius and center. Then, graph
the circle.
, center:
Equation:

Question

Write the standard form of the equation of the circle having the given radius and center. Then, graph the circle. $$ r=6 $$, center: $$ (0,0) $$ Equation:

UpStudy AI · Accepted Answer

**Equation:**

The standard form of the equation of a circle with center $$(h, k)$$ and radius $$r$$ is:

$$
(x - h)^2 + (y - k)^2 = r^2
$$

Given:
- Center $$(h, k) = (0, 0)$$
- Radius $$r = 6$$

Plugging these values into the standard form, we get:

$$
(x - 0)^2 + (y - 0)^2 = 6^2
$$
$$
x^2 + y^2 = 36
$$

**Graph:**

Below is a graphical representation of the circle with center at the origin $$(0, 0)$$ and radius $$6$$.

![Circle with center at (0,0) and radius 6](https://i.imgur.com/2c9ZfLc.png)

*If you prefer to plot it yourself, follow these steps:*

1. **Draw the Coordinate Axes:**
   - Draw a horizontal line (x-axis) and a vertical line (y-axis) intersecting at the origin $$(0, 0)$$.

2. **Plot the Center:**
   - Mark the center of the circle at the origin $$(0, 0)$$.

3. **Mark the Radius:**
   - From the center, measure 6 units in all four directions (up, down, left, right) to plot points $$(0, 6)$$, $$(0, -6)$$, $$(6, 0)$$, and $$(-6, 0)$$.

4. **Draw the Circle:**
   - Using a compass or a circular object, draw a smooth curve that passes through the plotted points, creating a circle.

**Key Features of the Circle:**
- **Center:** $$(0, 0)$$
- **Radius:** $$6$$
- **Diameter:** $$12$$ (since diameter = $$2 \times$$ radius)
- **Circumference:** $$2\pi r = 12\pi$$ units
- **Area:** $$\pi r^2 = 36\pi$$ square units

**Points on the Circle:**
Some points that lie on the circle include:
- $$(6, 0)$$
- $$(-6, 0)$$
- $$(0, 6)$$
- $$(0, -6)$$
- $$(3\sqrt{3}, 3)$$
- $$(-3\sqrt{3}, -3)$$, etc.

These points satisfy the equation $$x^2 + y^2 = 36$$.

**Visualization Tips:**
- Ensure your graph paper has enough space to accommodate the circle with radius $$6$$.
- Label the axes and mark equal intervals on both axes to maintain the circle's shape.
- A well-drawn circle should appear symmetrical around the center.
**Equation:** $$ x^2 + y^2 = 36 $$ **Graph:** A circle centered at the origin $$(0, 0)$$ with a radius of $$6$$ units.

Write the standard form of the equation of the circle having the given radius and center. Then, graph
the circle.
, center:
Equation:

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Latest Geometry Questions

Write the standard form of the equation of the circle having the given radius and center. Then, graph the circle. , center: Equation:

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Write the standard form of the equation of the circle having the given radius and center. Then, graph
the circle.
, center:
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