Q. 37 Use Cartesian coordinates to exp... [FREE SOLUTION]

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Chapter 9: Q. 37 (page 772)

Use Cartesian coordinates to express the equations for the ellipses determined by the conditions specified in Exercises 32鈥�37.
$foci (0, 卤伪), minor axis 2 伪$

Short Answer

Expert verified

The answer is $\frac{x^{2}}{伪^{2}} + \frac{y^{2}}{2 伪^{2}} = 1 .$

Step by step solution

Step 1. Given information.

The given values are,

$foci (0, 卤伪), minor axis 2 伪$ .

Step 2. values of the variables.

The foci are $(0, 伪) (0, - 伪)$

Centre $= (\frac{0 + 0}{2}, \frac{伪 - 伪}{2}) [since mid point = (\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})]$ $= (0, 0)$

$Given minor axis is 2 伪 . Then 2 b = 2 伪 b = 伪 c = \sqrt{(0 - 0)^{2} + (0 - 伪)^{2}} since D = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}] That is the distance from (0, 伪) (0, 0) . c = 伪 Now take c^{2} = a^{2} - b^{2} c^{2} = a^{2} - b^{2} 伪^{2} = a^{2} - 伪^{2} a^{2} = 2 伪^{2}$

Step 3. Substitution.

On substituting,

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

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91影视

Use Cartesian coordinates to express the equations for the ellipses determined by the conditions specified in Exercises 32鈥�37.
$foci (0, 卤伪), minor axis 2 伪$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. values of the variables.

Step 3. Substitution.

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91影视

Use Cartesian coordinates to express the equations for the ellipses determined by the conditions specified in Exercises 32鈥�37.foci(0,卤伪), minor axis2伪

Short Answer

Step by step solution

Step 1. Given information.

Step 2. values of the variables.

Step 3. Substitution.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Discrete Mathematics

Probability and Statistics

Mechanics Maths

Geometry

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Use Cartesian coordinates to express the equations for the ellipses determined by the conditions specified in Exercises 32鈥�37.
$foci (0, 卤伪), minor axis 2 伪$