   Chapter 10.5, Problem 41E

Chapter
Section
Textbook Problem

Find an equation for the conic that satisfies the given conditions.41. Ellipse, center (−1, 4), vertex (−1,0), focus (−1, 6)

To determine

To Find: The equation for the conic using the center (1,4) , focus (1,6) and the vertex (1,0) of the ellipse.

Explanation

Given:

The center (1,4) , focus (1,6) and the vertex (1,0) of the ellipse.

Calculation:

Since, the x coordinate of the focus and vertex is same and equal to 1 . Then the value of h is 1 and the foci and vertices are located in y axis.

Compute the value of c foci equation.

foci=(h,(k±c))

Substitute the value (1,4) for (h,k) and (1,6) for focus.

(1,6)=(h,(k+c))h=1(4+c)=6c=64c=±2

Therefore the value of c is ±2 .

Compute the value of a using the vertices equation:

vertices=(h,(k±a))

Substitute the value of (1,4) for (h,k) and (1,0) for vertex.

(1,0)=(1,(4±a))(4±a)=0a=±4

Therefore, the value of a is ±4

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Solve the equations in Exercises 126. x1x=0

Finite Mathematics and Applied Calculus (MindTap Course List)

Factor: 15b20

Elementary Technical Mathematics

For the following set of scores, find the value of each expression: a. X b. (X)2 c. X2 d. (X +3)

Essentials of Statistics for The Behavioral Sciences (MindTap Course List) 