Graphing Conic Sections Part 1: Circles

The video tutorial introduces conic sections, focusing on circles. It explains how conic sections are formed by intersecting a plane with a cone, and describes the concept of eccentricity. The tutorial then delves into graphing circles, deriving their equations, and using the method of completing the square to manipulate equations into standard form. The video concludes with a transition to the next topic, ellipses.

What is the eccentricity of a hyperbola?

• Between 0 and 1

• 1

• Greater than 1

• 0

How is a circle defined in a plane?

• As a set of points equidistant from a fixed point

• As a set of points equidistant from a line

• As a set of points equidistant from two points

• As a set of points equidistant from a curve

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

• (x - h)^2 + (y - k)^2 = r^2

• x^2 + y^2 = r^2

• x^2 - y^2 = r^2

• (x + h)^2 + (y + k)^2 = r^2

If a circle's equation is x^2 + y^2 = 9, where is its center?

• (0, 0)

• (1, 1)

• (3, 3)

• (9, 9)

For the equation (x - 2)^2 + (y - 3)^2 = r^2, what is the center of the circle?

• (2, 3)

• (-3, -2)

• (-2, -3)

• (3, 2)

What technique is used to rearrange the equation x^2 + y^2 + 4x - 6y - 23 into standard form?

• Substitution

• Using the quadratic formula

• Factoring

• Completing the square

After completing the square for x^2 + y^2 + 4x - 6y - 23, what is the center of the circle?

• (3, -2)

• (2, -3)

• (-3, 2)

• (-2, 3)