Chapter 10: Q 62. (page 655)

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

Short Answer

Expert verified

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

Step by step solution

. Given information.

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

Since the center and the focus lie on the line $x = 1$ , thus the major axis is parallel to the y-axis.

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

Since, the point $(2, 2)$ lies on the ellipse

$\frac{{(2 - 1)}^{2}}{b^{2}} + \frac{{(2 - 2)}^{2}}{a^{2}} = 1 b^{2} = 1$

Step 2. The equation of ellipse.

Substitute $c = 2$ and $a = 1$ we get.

$b^{2} = a^{2} - c^{2} a^{2} = b^{2} + c^{2} a^{2} = 1 + 4 a^{2} = 5$

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

Step 3. 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 $(1, 4)$ : contains the point $(2, 2)$

Short Answer

Step by step solution

. Given information.

Step 2. The equation of ellipse.

Step 3. 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(1,4): contains the point(2,2)

Short Answer

Step by step solution

. Given information.

Step 2. The equation of ellipse.

Step 3. Graph of the ellipse .

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Applied Mathematics

Discrete Mathematics

Statistics

Theoretical and Mathematical Physics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

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