Circle Equations and Properties

This video tutorial covers writing equations of circles, including identifying the center and radius. It provides examples of solving circle equations and introduces the concept of completing the square, which is applied to circle equations. The tutorial also explains how to convert equations to standard form and solve quadratic equations using completing the square.

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

• (x + h)^2 + (y + k)^2 = r^2

• x^2 + y^2 = r^2

• (x - h)^2 + (y - k)^2 = r^2

• x^2 + y^2 + 2hx + 2ky = r^2

If the center of a circle is at (-1, 2) and the radius is 14, what is the equation of the circle?

• (x - 1)^2 + (y + 2)^2 = 196

• (x + 1)^2 + (y + 2)^2 = 14

• (x - 1)^2 + (y - 2)^2 = 14

• (x + 1)^2 + (y - 2)^2 = 196

How do you determine the center of a circle when given two intersecting diameters?

• The center is at the midpoint of the radius.

• The center is at the endpoint of one diameter.

• The center is at the intersection of the diameters.

• The center is at the midpoint of one diameter.

Given the area of a circle as 16π, what is the radius?

• 2

• 4

• 8

• 16

What is the formula for the circumference of a circle?

• 2πr

• 2πd

• πr^2

• πd

What is the purpose of completing the square in algebra?

• To solve linear equations

• To convert quadratic equations into a form that can be easily solved

• To factor polynomials

• To simplify fractions

In completing the square, what value is added to both sides of the equation?

• b/2

• b^2

• (b/2)^2

• 2b

What is the result of completing the square for x^2 - 8x?

• (x + 8)^2

• (x + 4)^2

• (x - 4)^2

• (x - 8)^2

How do you find the center of a circle from its equation in standard form?

• The constants added to x and y

• The square root of the radius

• The coefficients of x and y

• The opposite of the constants in the equation

What is the radius of a circle if its equation is (x - 6)^2 + (y - 1)^2 = 49?

• 6

• 7

• 8

• 49