Chapter 9: Q. 33 (page 772)

Use Cartesian coordinates to express the equations for the ellipses determined by the conditions specified in Exercises 32–37.
$foci (\pm \sqrt{5}, 1), major axis 6$

Short Answer

Expert verified

The equation is $\frac{x^{2}}{9} + \frac{(y - 1)^{2}}{4} = 1 .$

Step by step solution

Step 1. Given information.

The given values are ,

$foci (\pm \sqrt{5}, 1), major axis 6$

Step 2. Value of variables.

The foci are $(\sqrt{5}, 1) (- \sqrt{5}, 1)$

$center = (\frac{\sqrt{5} - \sqrt{5}}{2}, \frac{1 + 1}{2}) = (0, 1)$

$G i v e n, 2 a = 6 a = 3 c = \sqrt{(0 - \sqrt{5})^{2} + (1 - 1)^{2}} [since D = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}] That is the distance from (\sqrt{5}, 1) (0, 1) . c = \sqrt{5} c^{2} = a^{2} - b^{2} (\sqrt{5})^{2} = 3^{2} - b^{2} b^{2} = 4$

Step 3. Substitution.

On substituting all the obtained values in,

$\frac{(x - h)^{2}}{a^{2}} + \frac{(y - k)^{2}}{b^{2}} = 1 where a > b, (h, k) is the center. \frac{(x - 0)^{2}}{9} + \frac{(y - 1)^{2}}{4} = 1 \frac{x^{2}}{9} + \frac{(y - 1)^{2}}{4} = 1$

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Use Cartesian coordinates to express the equations for the ellipses determined by the conditions specified in Exercises 32–37.
$foci (\pm \sqrt{5}, 1), major axis 6$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Value of variables.

Step 3. Substitution.

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Use Cartesian coordinates to express the equations for the ellipses determined by the conditions specified in Exercises 32–37.foci(±5,1), major axis6

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Value of variables.

Step 3. Substitution.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Probability and Statistics

Theoretical and Mathematical Physics

Geometry

Calculus

Logic and Functions

Study anywhere. Anytime. Across all devices.

Use Cartesian coordinates to express the equations for the ellipses determined by the conditions specified in Exercises 32–37.
$foci (\pm \sqrt{5}, 1), major axis 6$