Chapter 10: Q. 38 (page 654)

Find an equation for each ellipse. Graph the equation by hand.
Vertices at $(\pm 5, 0); c = 2$

Short Answer

Expert verified

The equation of ellipse is $\frac{x^{2}}{25} + \frac{y^{2}}{24} = 1$ and the graph is

Step by step solution

Step 1. Given Information

We are given vertices as $(\pm 5, 0); c = 2$

Step 2. Calculation

The vertices lie on the x-axis. So, the major axis of the ellipse is x-axis and the center lies at the midpoint of vertices that is at origin.

The foci are $(\pm 1, 0)$ and the distance from center from one of the vertices is $a = 4$ . Thus, we have,

$b^{2} = a^{2} - c^{2} b^{2} = 25 - 1 b^{2} = 24$

Thus, the equation of ellipse is as follows,

$\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1 \frac{x^{2}}{25} + \frac{y^{2}}{24} = 1$

On plotting the points on the graph, we get,

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Find an equation for each ellipse. Graph the equation by hand.
Vertices at $(\pm 5, 0); c = 2$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

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Find an equation for each ellipse. Graph the equation by hand.Vertices at±5,0;c=2

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Theoretical and Mathematical Physics

Pure Maths

Mechanics Maths

Decision Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Find an equation for each ellipse. Graph the equation by hand.
Vertices at $(\pm 5, 0); c = 2$