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Pearson Algebra 2 Common Core, 2011

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Pearson Algebra 2 Common Core, 2011 View details

6. Translating Conic Sections

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Exercise 1 Page 658

Identify the type of ellipse. Horizontal ellipses fit the equation $\frac{( x - h ) ^{2}}{a ^{2}} + \frac{( y - k ) ^{2}}{b ^{2}} = 1,$ and vertical ellipses fit the equation $\frac{( x - h ) ^{2}}{b ^{2}} + \frac{( y - k ) ^{2}}{a ^{2}} = 1 .$ In both cases, $a$ and $b$ are positive numbers such that $a > b .$

Center: $(- 7, - 1)$
Vertices: $(8, - 1)$ and $(- 22, - 1)$
Foci: $(2, - 1)$ and $(- 16, - 1)$

Practice makes perfect

We want to identify the center, vertices, and foci of the ellipse. To do so, we will rewrite the given equation just a little bit.

\frac{( x + 7 ) ^{2}}{2 2 5} + \frac{( y + 1 ) ^{2}}{1 4 4} = 1

Write as a power

\frac{( x + 7 ) ^{2}}{1 5 ^{2}} + \frac{( y + 1 ) ^{2}}{1 2 ^{2}} = 1

$a = - (- a)$

\frac{( x - ( - 7 ) ) ^{2}}{1 5 ^{2}} + \frac{( y - ( - 1 ) ) ^{2}}{1 2 ^{2}} = 1

Notice that the denominator of the expression containing the

x -

variable is greater than the denominator of the expression that contains the

y -

variable. Therefore, we have a horizontal ellipse. Let's recall the main characteristics of this type of ellipse.

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Subchapter links

Lesson Check p.658

Practice and Problem-Solving Exercises p.658-660

Standardized Test Prep p.660

Mixed Review p.660