Finding the Center and Radius of a Circle

This video tutorial explains how to find the center and radius of a circle from its equation. It covers the standard format of a circle equation, how to identify the radius and center, and the importance of correctly interpreting signs in the equation. The tutorial provides a step-by-step guide to calculating the radius and determining the center, emphasizing the need to rewrite plus signs as minus negatives when necessary.

What indicates that an equation represents a circle?

• Both x and y variables are squared and summed.

• The presence of x and y variables squared.

• The equation includes a plus sign.

• The equation is equal to a number.

What is the general form of a circle's equation used to identify its center and radius?

• R^2 = (x - h)^2 + (y - k)^2

• x^2 + y^2 + R^2 = 0

• (x - h)^2 + (y - k)^2 = R^2

• x^2 + y^2 = R^2

How do you find the radius of a circle from its equation?

• Square root the number the equation equals.

• Divide the equation by 2.

• Multiply the x and y coefficients.

• Add the x and y coefficients.

What is the radius of a circle if R squared equals 36?

• 18

• 6

• 12

• 36

Why is the radius of a circle always positive?

• Because it is squared in the equation.

• Because it cannot be zero.

• Because it represents a distance.

• Because it is derived from the equation's constant.

How is the center of a circle represented in its equation?

• By the equation's constant term.

• By the numbers subtracted from x and y.

• By the square root of the radius.

• By the coefficients of x and y.

What does the center (9, -7) indicate in a circle's equation?

• The circle touches the x-axis at 9 and y-axis at -7.

• The circle is 9 units above and 7 units to the left of the origin.

• The circle's center is located at 9 units right and 7 units down from the origin.

• The radius of the circle is 9.

What must you be cautious of when determining the center of a circle from its equation?

• The radius of the circle.

• The coefficient of the x and y squared terms.

• The signs in front of the x and y terms.

• The equation's constant term.

If a circle's equation is written with a plus sign, how should you interpret it for finding the center?

• As a subtraction from both x and y.

• As an addition to both x and y.

• Rewrite the plus as minus a negative.

• Ignore the plus sign.