Graphing and Writing Circle Equations

This video tutorial covers writing and graphing equations of circles. It begins with an introduction to the objectives, which include writing the equation of a circle and graphing it. The standard equation of a circle is explained, followed by examples demonstrating how to find the center and radius from an equation. The video also covers using the distance formula to find the radius and write circle equations. Steps for graphing a circle from its equation are provided, along with methods for writing equations from graphs. The tutorial concludes with a problem-solving exercise to determine if a point lies on a circle.

What is the standard form of a circle's equation in a coordinate plane?

• r = (x + h) + (y + k)

• r = (x - h)^2 + (y - k)^2

• r^2 = (x - h)^2 + (y - k)^2

• r^2 = (x + h)^2 + (y + k)^2

What information is essential to write the equation of a circle?

• Radius and center

• Diameter and circumference

• Area and diameter

• Circumference and area

How do you determine the center of a circle from its equation?

• Add the values inside the parentheses

• Subtract the values inside the parentheses

• Flip the signs of the values inside the parentheses

• Multiply the values inside the parentheses

What is the radius of a circle if its equation includes a term 'r^2 = 25'?

• 50

• 5

• 625

• 25

How do you find the radius if you know a point on the circle and the center?

• Use the midpoint formula

• Multiply the coordinates of the center by those of the point

• Use the distance formula

• Subtract the coordinates of the point from the center

What is the first step in graphing a circle from an equation?

• Draw the circle

• Calculate the diameter

• Identify the center and radius

• Plot points in each cardinal direction

How do you verify if a point lies on a circle given its equation?

• Substitute the point's coordinates into the equation and check if it holds true

• Calculate the distance from the point to the center

• Compare the point's coordinates to the circle's diameter

• Ensure the point's coordinates are integers

What method is used to find the center of a circle when given the endpoints of its diameter?

• Distance formula

• Circumference formula

• Midpoint formula

• Radius calculation

If the endpoints of a diameter are (2, -4) and (0, 10), what is the center of the circle?

• (2, -3)

• (2, 3)

• (1, -3)

• (1, 3)

What is the correct equation of a circle with a center at (5, 0) and a radius of 10?

• (x - 5)^2 + y^2 = 100

• (x + 5)^2 + y^2 = 10

• (x + 5)^2 + y^2 = 100

• (x - 5)^2 + y^2 = 10