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Chapter 10: Q. 9 (page 654)

For the ellipse x24+y225=1, the vertices are the points _____ and _____.

Short Answer

Expert verified

For the ellipse x24+y225=1, the vertices are the points (0,-5)and(0,5).

Step by step solution

01

Step 1. Given Information.

We want to fill the gap in the given equation with the missing terms.

02

Step 2. Method to find:

We know that

If an ellipse is given with the following equation:

x2b2+y2a2=1

where a>b, then it is centred at the origin, the major axis is the y-axis and the parameters aandbrepresent its width 2aand its height 2b.

Since the vertices lie on the major axis and the segment connecting them is the width of the ellipse, then it is 2along.

Therefore, the vertices are the points(0,-a)and(0,a)

03

Step 3. Solution:

The following equation is given

x24+y225=1

then by comparing it to the equation of an ellipse given in Step 2. we can see that

Since 22=4and because 25>4鈬�5>2

Therefore, the vertices are points:

V1=(0,-5)andV2=(0,5)

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Most popular questions from this chapter

In Problems 15鈥�18, the graph of a hyperbola is given. Match each graph to its equation.

Equations:

Ax24-y2=1Bx2-y24=1Cy24-x2=1Dy2-x24=1

Graph:

The point that is symmetric with respect to the x-axis to the point (-2, 5) is ________.

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

Center at (2,-2): vertex at (7,-2): focus at(4,-2).

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

Vertices at (4,3)and (4,9): focus at(4,8).

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

x2=-4y
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