Understanding Circles in Standard Form

This video tutorial explains how to graph a circle given in standard form. It covers the standard form equation, identifying the center and radius of the circle, and provides a step-by-step guide to plotting the circle on a graph. The tutorial emphasizes understanding the signs in the equation and calculating the radius from R squared.

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

• X^2 + Y^2 = R^2

• (X + H)^2 + (Y + K)^2 = R^2

• (X - H)^2 + (Y - K)^2 = R^2

• X^2 + Y^2 + 2X + 2Y = R^2

If the equation of a circle is (X - 2)^2 + (Y + 3)^2 = 16, what is the X-coordinate of the center?

• -2

• 2

• -3

• 3

In the equation (X - 2)^2 + (Y + 3)^2 = 16, what is the Y-coordinate of the center?

• 3

• 2

• -3

• -2

Why are the signs of the coordinates in the circle's equation opposite to what they appear?

• Because the equation is in slope-intercept form

• Because the equation is in standard form

• Because the equation is in vertex form

• Because the equation is in factored form

What is the radius of a circle if the equation is (X - 2)^2 + (Y + 3)^2 = 16?

• 4

• 3

• 2

• 5

How do you find the radius from the equation (X - H)^2 + (Y - K)^2 = R^2?

• R is the square root of the right side

• R is the right side multiplied by 2

• R is the square of the right side

• R is the right side divided by 2

What is the first step in graphing a circle given its equation?

• Plot the center

• Plot the radius

• Calculate the diameter

• Draw the circle

If the center of a circle is at (2, -3) and the radius is 4, which point is on the circle?

• (2, 1)

• (6, -3)

• (2, -7)

• All of the above

How many units do you move from the center to find points on the circle?

• Equal to the circumference

• Equal to the diameter

• Equal to the area

• Equal to the radius

What is the relationship between the center and any point on the circle?

• The distance is equal to the circumference

• The distance is equal to the area

• The distance is equal to the radius

• The distance is equal to the diameter