Chapter 10: Q 60. (page 655)

Find an equation for each ellipse. Graph the equation by hand.
Vertices at $(2, 5)$ and $(2, - 1)$ :c=2

Short Answer

Expert verified

The equation of the ellipse is $\frac{{(x - 2)}^{2}}{5} + \frac{{(y - 2)}^{2}}{9} = 1$ and graph of the ellipse is

Step by step solution

Step 1. Given information.

Vertices at $(2, 5)$ and $(2, - 1)$ : $c = 2$

The vertices lies on the line $x = 2$ , thus the major axis is parallel to the y-axis.

The center is at the mid point of the vertices $(2, 2)$ .

The distance of the center from one of the foci is $c = 2$ .

The distance of the center from one of the vertices is $a = 3$ .

Step 2. The equation of ellipse.

Substitute $a = 3$ and $c = 2$ in $b^{2} = a^{2} - c^{2}$ we get.

$b^{2} = a^{2} - c^{2} b^{2} = 9 - 4 b^{2} = 5$

Substituting the values of $a^{2}$ and $b^{2}$ in the equation of the ellipse we get.

$\frac{{(x - 2)}^{2}}{5} + \frac{{(y - 2)}^{2}}{9} = 1$

.Graph of the ellipse .

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Find an equation for each ellipse. Graph the equation by hand.
Vertices at $(2, 5)$ and $(2, - 1)$ :c=2

Short Answer

Step by step solution

Step 1. Given information.

Step 2. The equation of ellipse.

.Graph of the ellipse .

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Find an equation for each ellipse. Graph the equation by hand. Vertices at(2,5)and(2,-1):c=2

Short Answer

Step by step solution

Step 1. Given information.

Step 2. The equation of ellipse.

.Graph of the ellipse .

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Geometry

Decision Maths

Calculus

Mechanics Maths

Statistics

Study anywhere. Anytime. Across all devices.

Find an equation for each ellipse. Graph the equation by hand.
Vertices at $(2, 5)$ and $(2, - 1)$ :c=2