Chapter 9: Q. 32 (page 772)

Use Cartesian coordinates to express the equations for the ellipses determined by the conditions specified in Exercises 32–37.
$foci (\pm 1, 0), major axis 4$

Short Answer

Expert verified

The equation is $\frac{x^{2}}{4} + \frac{y^{2}}{3} = 1 .$

Step by step solution

Step 1. Given information.

We are given,

$foci (\pm 1, 0), major axis 4$

Step 2. Value of the variables.

The focus points are $(1, 0) (- 1, 0)$ .

The center which is the midpoint of the focus points is,

$= (\frac{1 - 1}{2}, 0) [since mid point = (\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})] = (0, 0) Given major axis is 4 . Then 2 a = 4 a = 2 N o w, c = \sqrt{(1 + 0)^{2} + (0 - 0)^{2}} [since D = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}] c = 1 N o w, A g a i n, c^{2} = a^{2} - b^{2} 1 = 4 - b^{2} b^{2} = 3$

Step 3. Substitution.

On substituting the obtained values,

$\frac{(x - h)^{2}}{a^{2}} + \frac{(y - k)^{2}}{b^{2}} = 1 where a > b, (h, k) is the center. \frac{(x - 0)^{2}}{4} + \frac{(y - 0)^{2}}{3} = 1 \frac{x^{2}}{4} + \frac{y^{2}}{3} = 1$

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Use Cartesian coordinates to express the equations for the ellipses determined by the conditions specified in Exercises 32–37.
$foci (\pm 1, 0), major axis 4$

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.foci(±1,0),major axis4

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

Geometry

Pure Maths

Logic and Functions

Probability and Statistics

Theoretical and Mathematical Physics

Applied Mathematics

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.
$foci (\pm 1, 0), major axis 4$