Chapter 10: Q 61. (page 655)

Find an equation for each ellipse. Graph the equation by hand.
Center at $(1, 2)$ : focus at $(4, 2)$ : contains the point $(1, 3)$

Short Answer

Expert verified

The equation of the ellipse is $\frac{{(x - 1)}^{2}}{10} + {(y - 2)}^{2} = 1$ and graph of the ellipse is

Step by step solution

. Given information.

Center at $(1, 2)$ : focus at $(4, 2)$ : contains the point $(1, 3)$

By using distance formula the value of $a$ is

$a = \sqrt{{(4 - 1)}^{2} + {(2 - 3)}^{2}} a = \sqrt{9 + 1} a = \sqrt{10}$

Since $a = \sqrt{10}$ and the major axis is parallel to the x-axis, the vertices are $\sqrt{10}$ units to the left and right of the center.

Thus, the vertices are $v_{1} = (1 + \sqrt{10}, 2)$ and $v_{2} = (1 - \sqrt{10}, 2)$ .

The distance between the center and the focus will give the value of $c$ .

$c = \sqrt{{(4 - 1)}^{2} + {(2 - 2)}^{2}} c = \sqrt{9} c = 3$

Step 2. The equation of ellipse.

Substituting $c = 3$ and $a = \sqrt{10}$ we get.

localid="1646723555627" $b^{2} = {(\sqrt{10})}^{2} - {(3)}^{2} b^{2} = 10 - 9 b^{2} = 1$

The equation of the ellipse is $\frac{{(x - 1)}^{2}}{10} + {(y - 2)}^{2} = 1$

.Graph of the ellipse .

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Find an equation for each ellipse. Graph the equation by hand.
Center at $(1, 2)$ : focus at $(4, 2)$ : contains the point $(1, 3)$

Short Answer

Step by step solution

. 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. Center at (1,2): focus at (4,2): contains the point(1,3)

Short Answer

Step by step solution

. 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

Mechanics Maths

Decision Maths

Geometry

Statistics

Calculus

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Find an equation for each ellipse. Graph the equation by hand.
Center at $(1, 2)$ : focus at $(4, 2)$ : contains the point $(1, 3)$