Sketch the Graph of the Circle (x - 6)^2 + (y - 7)^2 = 1 and Find Domain, Range MyMathlab Homework

TL;DR

Learn how to graph a circle equation, find its center and radius, and determine the domain and range.

Transcript

and this problem were asked to give the center and radius of the circle described by the equation and then graph the equation so the equation in this problem is X minus 6 quantity squared plus y minus 7 quantity squared equals 1 so the center radius form or standard form of a circle looks like this X minus H squared plus y minus K squared equals R ... Read More

Key Insights

• 👈 The equation (x - h)^2 + (y - k)^2 = r^2 represents a circle in standard form, with the center at point (h, k) and a radius of r.
• 👉 Graphing a circle equation by hand involves plotting the center point and then moving one unit up, down, left, and right to mark points on the circle.
• 😥 Using software, the circle equation can be graphed by selecting the circle tool and plotting the center point, followed by a point one unit away.

Questions & Answers

Q: What is the center and radius of the circle described by the equation?

The center of the circle is located at the point (6, 7), and the radius is equal to 1 unit.

Q: How do you graph a circle equation by hand?

To graph the circle equation by hand, plot the center point (6, 7), and then move one unit up, down, left, and right to plot points on the circle. Connect these points to form a circular shape.

Q: How can the circle equation be graphed using software?

In software, select the circle tool, plot the center point (6, 7), and then plot a point one unit away. The software will automatically generate the circle.

Q: What is the domain and range of the circle equation?

The domain is all the x-values, ranging from 5 to 7. The range is all the y-values, ranging from 6 to 8.

Summary & Key Takeaways

• The equation provided is in the form (x - 6)^2 + (y - 7)^2 = 1, representing a circle with a center at (6, 7) and a radius of 1.

• To graph this equation by hand, plot the center point (6, 7) and then move one unit up, down, left, and right to mark points on the circle, connecting them to form the circle.

• Alternatively, using software, select the circle tool, plot the center point (6, 7), and then plot a point one unit away to complete the circle.