Chapter 11: Q. 115 (page 1119)

In the following exercises, graph each ellipse.
$\frac{{(x + 1)}^{2}}{4} + \frac{{(y + 6)}^{2}}{25} = 1$

Short Answer

Expert verified

The graph of the ellipse is

Step by step solution

Step 1.Given information

The equation of the ellipse is $\frac{{(x + 1)}^{2}}{4} + \frac{{(y + 6)}^{2}}{25} = 1$

Step 2.Concept used

The standard form of the ellipse with center not at the origin is

$\frac{{(x - h)}^{2}}{a^{2}} + \frac{{(y - k)}^{2}}{b^{2}} = 1 Center (h, k), a > b \Rightarrow majoraxisishorizantal,sothedistancefromthecentertothevertexis a . b > a \Rightarrow major axis is vertical, so the distance from the center to the vertex is b .$

Step 3. Find the center and major axis

The equation of the ellipse is $\frac{{(x + 1)}^{2}}{4} + \frac{{(y + 6)}^{2}}{25} = 1$

Center $(h, k) = (- 1, - 6)$

$25 > 4 \Rightarrow majoraxisisvertical a^{2} = 4 \Rightarrow a = \pm 2 Thedistancefromcentertoendpointsofminoraxisis 2 b^{2} = 25 \Rightarrow b = \pm 5 Thedistancefromcentertoendpointsofmajoraxisis 5$

Step 4. Sketch the ellipse

The graph of the ellipse is

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In the following exercises, graph each ellipse.
$\frac{{(x + 1)}^{2}}{4} + \frac{{(y + 6)}^{2}}{25} = 1$

Short Answer

Step by step solution

Step 1.Given information

Step 2.Concept used

Step 3. Find the center and major axis

Step 4. Sketch the ellipse

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In the following exercises, graph each ellipse.x+124+y+6225=1

Short Answer

Step by step solution

Step 1.Given information

Step 2.Concept used

Step 3. Find the center and major axis

Step 4. Sketch the ellipse

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Discrete Mathematics

Decision Maths

Applied Mathematics

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Study anywhere. Anytime. Across all devices.

In the following exercises, graph each ellipse.
$\frac{{(x + 1)}^{2}}{4} + \frac{{(y + 6)}^{2}}{25} = 1$