 # Chapter 10 10.1 Distance and Midpoint Formula Goal 1 To find the distance between two points in a plane Goal 2 To find the coordinates of the midpoint.

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Chapter 10 10.1 Distance and Midpoint Formula Goal 1 To find the distance between two points in a plane Goal 2 To find the coordinates of the midpoint of a segment given the endpoints

HW #10.1 Pg 431-432 1-15 Odd, 17-27

Chapter 10 10.2 Conic Sections Circles Goal 1 To find the equation of a circle given the radius and the coordinates of the center of the circle. Goal 2 To find the radius and coordinates of the center of the circle given the equation of the circle

CircleEllipse HyperbolaParabola

C F D B EA

HW #10.2 Pg 436-437 1-15 odd, 16-26, 28-31

Chapter 10 10.3 Ellipses

c 2 = a 2 – b 2 Center of the Ellipse

Identify the center, vertices and foci.

HW #10.3 Pg 442-443 1-23 Odd, 25-34

Chapter 10 10.4 Hyperbolas

HW #10.4 Pg 450-451 1-23 Odd, 24-30

Chapter 10 10.5 Parabolas

Definition: Parabola The set of all points in a plane that are equidistant from a fixed point F and a fixed line. The point is the Focus and the line is the Directrix

The book uses p for a so it would be y 2 = 4px

Theorem 10-10 A parabola with focus at (0, p) and vertex at (0, 0) has directrix y = -p Theorem 10-11 The standard form of a parabola with focus at (0, p), directrix y = -p, vertex (0, 0), and y-axis as the only line of symmetry is x 2 = 4py Theorem 10-11 The standard form of a parabola with focus at (p, 0), directrix x = -p, vertex (0, 0), and x-axis as the only line of symmetry is y 2 = 4px

The vertex is midway between the focus and the directrix

Write the standard form of the equation of the parabola that satisfies the given conditions Focus: (4, 0); Directrix x = -4 y 2 = 16x Focus: (-4, 2); Directrix x = -6 (y - 2) 2 =4(x + 5) Focus: (-4, 2); Vertex (-4, 5) (x + 4) 2 =-12(y - 5)

HW #10.5 Pg 456-457 1-37 Odd, 38-41

Chapter 10 10.6 Second Degree Equations and Systems

hyperbola parabola ellipse circle hyperbola

The solutions appear to be (4,3) and (-4,-3).

The solutions appear to be (5,0) and (-5,0).

(4, 3) and (-3, -4) (4, 7) and (-1, 2) (-2, 0) and (2, 0) (4, 0) and (-4, 0)

HW #10.6 Pg 462-463 1-39 Odd 41-43

Chapter 10 10.7 Solving Quadratic Systems Algebraically

Substitute x = 2 and x = -3 into the linear equation and solve for y.

Find the points of intersection of the graphs in the system

Because Equation 2 has no x 2 -term, solve that equation for x. Next, substitute 2y 2 - 2 for x in Equation 1 and solve for y.

You can eliminate the y 2 -term by adding the two equations.

Find the points of intersection of the graphs in the system.

HW #10.7 Pg 467-468 1-25 Odd, 26-30

Chapter 10 10.8 Using Systems of Second Degree Equations

Two square pieces of plastic together have an area of 100 square inches. When a square the size of the smaller piece is cut from the larger piece, the remaining area is 28 square inches. What are the lengths of the sides of the two squares? Larger Square is 8 x 8 Smaller Square is 6 x 6

A rectangular beam with a cross-sectional area 48 in 2 is cut from a circular log with diameter 10 inches. Find the dimensions of the beam. 6 x 8

The epicenter of the earthquake is 50 miles due west of the first seismograph

HW #10.8 Pg 471 10-18

Test Review

The pedals of a bicycle drive a chain wheel, which drives a smaller sprocket wheel on the rear axle. Many chainwheels are circular. However, some are slightly elliptical, which tends to make pedaling easier. The front chain wheel on the bicycle shown below is 8 inches at its widest and 7½ inches at its narrowest. 1.Find an equation for the outline of this elliptical chain wheel. 2.What is the area of the chain wheel.

HW #R-10 Pg 475-477 1-33 Odd

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