Conic Sections and Their Properties

The video tutorial by Tom Atwater explores conic sections, focusing on circles and parabolas. It begins with an introduction to conic sections derived from a cone, including circles, ellipses, parabolas, and hyperbolas. The tutorial then delves into circle equations, demonstrating how to graph them by hand and using a calculator. It covers completing the square to identify circle equations. The focus shifts to parabolas, explaining their properties, graphing techniques, and equations. The tutorial concludes with translations of parabolas, showing how to find and graph their equations.

What is a conic section derived from?

• A cube

• A cone

• A cylinder

• A sphere

Which shape is formed when a plane intersects a cone perpendicular to its axis?

• Ellipse

• Parabola

• Hyperbola

• Circle

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, 4) and a radius of 6, what is its equation?

• (x+3)^2 + (y+4)^2 = 36

• (x-3)^2 + (y-4)^2 = 36

• (x-3)^2 + (y+4)^2 = 36

• (x+3)^2 + (y-4)^2 = 36

What is the domain of a circle with center (-3, 4) and radius 6?

• [-9, 3]

• [-3, 9]

• [3, 9]

• [-6, 6]

What is a challenge of using a graphing calculator for circles?

• It requires complex equations

• It only graphs ellipses

• It graphs circles as two semicircles

• It cannot graph circles

How do you identify a circle from the equation x^2 - 6x + y^2 + 10y + 25 = 0?

• By factoring

• By using the quadratic formula

• By completing the square

• By graphing

What is the focus of a parabola with the equation x^2 = 4Cy?

• (0, -C)

• (C, 0)

• (-C, 0)

• (0, C)

For a parabola with a vertical axis, what is the directrix?

• y = C

• y = -C

• x = -C

• x = C

What is the vertex of a parabola with the equation x^2 = 8y?

• (0, 0)

• (0, 2)

• (2, 0)

• (0, -2)