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Chapter 10: Q. 36 (page 654)

Find an equation for each ellipse. Graph the equation by hand.

Vertices at±4,0, y-intercepts are±1

Short Answer

Expert verified

The equation of ellipse is x216+y21=1and the graph is

Step by step solution

01

Step 1. Given Information

We are given vertices and y-intercept as±4,0and±1

02

Step 2. Calculation

The major axis of the ellipse is the x-axis and the center is at the midpoint of vertices which is the origin. From the given y-intercepts, we have, b=1and the distance of the center from one of the vertices is a=4

Find the value of foci using the formula.

c2=a2-b2c2=16-1c2=15

Thus, the equation of ellipse is as follows,

x2a2+y2b2=1x216+y21=1

On plotting the points on the graph, we get,

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Most popular questions from this chapter

Find the intercepts of the equation y2=16-4x2.

Find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation by hand.

Vertex at 0,0, axis of symmetry is the x-axis; containing the point2,3.

Find the vertex, focus, and directrix of each parabola. Graph the equation by hand. Verify your graph using a graphing utility.

y2=-16x

The graph of a parabola is given. Match each graph to its equation.

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A(n)__________ is the collection of all points in the plane such that the distance from each point to a fixed point equals its distance to a fixed line.
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