Chapter 9: Q. 35 (page 772)

Use Cartesian coordinates to express the equations for the ellipses determined by the conditions specified in Exercises 32–37.
$foci (0, \pm \frac{3 \sqrt{3}}{2}), minor axis 3$

Short Answer

Expert verified

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

Step by step solution

Step 1. Given information.

We are given,

$foci (0, \pm \frac{3 \sqrt{3}}{2}), minor axis 3$

Step 2. Value of the variables.

The foci are $(0, \frac{3 \sqrt{3}}{2}) (0, - \frac{3 \sqrt{3}}{2})$

$center = (\frac{0 + 0}{2}, \frac{\frac{3 \sqrt{3}}{2} - \frac{3 \sqrt{3}}{2}}{2}) [since mid point = (\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})] center = (0, 0) Given minor axis is 3 . Then 2 b = 3 b = \frac{3}{2} c = \sqrt{(0 - 0)^{2} + {(0 - \frac{3 \sqrt{3}}{2})}^{2}} [since D = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}] That is the distance from (0, \frac{3 \sqrt{3}}{2}) (0, 0) . c = \frac{3 \sqrt{3}}{2} Now take c^{2} = a^{2} - b^{2} {(\frac{3 \sqrt{3}}{2})}^{2} = a^{2} - {(\frac{3}{2})}^{2} \frac{27}{4} = a^{2} - \frac{9}{4} a^{2} = 9$

Step 3. Substitution.

Now, substitute the obtained values,

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

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Use Cartesian coordinates to express the equations for the ellipses determined by the conditions specified in Exercises 32–37.
$foci (0, \pm \frac{3 \sqrt{3}}{2}), minor axis 3$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Value of the 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.foci0,±332, minor axis3

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Value of the variables.

Step 3. Substitution.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Discrete Mathematics

Geometry

Decision Maths

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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.
$foci (0, \pm \frac{3 \sqrt{3}}{2}), minor axis 3$