Graphing Circles and Conic Sections

The video tutorial by Tom Atwater explores the concepts of circles and parabolas, starting with real-life applications of parabolas. It delves into conic sections derived from a cone, including circles, ellipses, parabolas, and hyperbolas. The tutorial provides a detailed explanation of circles, their equations, and how to graph them both manually and using a graphing calculator. The video emphasizes understanding the domain and range of circles and demonstrates the use of TI-84 and TI-83 calculators for graphing.

Which of the following is NOT a real-life application of parabolas?

• Shooting a basketball

• Throwing a football

• Designing a parachute

• Flying a kite

What is a conic section?

• A shape derived from a cylinder

• A shape derived from a cone

• A shape derived from a sphere

• A shape derived from a cube

How is a circle formed from a cone?

• By intersecting a plane perpendicular to the cone's axis

• By intersecting a plane parallel to the cone's axis

• By intersecting a plane at the cone's base

• By intersecting a plane at an angle other than 90 degrees

What angle is required to form an ellipse from a cone?

• 180 degrees

• Any angle other than 90 degrees

• 45 degrees

• 90 degrees

Which conic section is formed when a plane intersects a cone and does not pass through both sides?

• Hyperbola

• Parabola

• Circle

• Ellipse

What is the defining characteristic of a hyperbola?

• A plane intersects only one side of the cone

• A plane is parallel to the cone's axis

• A plane intersects the cone's base

• A plane is perpendicular to the cone's base

What is the equation of a circle with center (h, k) and radius r?

• (x + h)^2 - (y + k)^2 = r^2

• (x + h)^2 + (y + k)^2 = r^2

• (x - h)^2 - (y - k)^2 = r^2

• (x - h)^2 + (y - k)^2 = r^2

If a circle has a center at (3, -1) and a radius of 2, what is its equation?

• (x - 3)^2 - (y + 1)^2 = 4

• (x + 3)^2 + (y - 1)^2 = 4

• (x + 3)^2 - (y - 1)^2 = 4

• (x - 3)^2 + (y + 1)^2 = 4

What is the center of a circle with the equation (x + 3)^2 + (y - 4)^2 = 36?

• (-3, -4)

• (3, 4)

• (3, -4)

• (-3, 4)

What is the radius of a circle with the equation (x + 3)^2 + (y - 4)^2 = 36?

• 6

• 3

• 12

• 9