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Chapter 10: Q. 33 (page 654)

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

Focus at-4,0, vertices at卤5,0

Short Answer

Expert verified

The equation of ellipse is x225+y29=1and the graph is

Step by step solution

01

Step 1. Given Information

We are given Focus and vertices as -4,0and卤5,0 respectively.

02

Step 2. Calculation

Since the given vertices and focus lies on the x-axis then the x-axis is the major axis. The center is the midpoint of the vertices (-5,0)and(5,0)whichis(0,0)

The distance from the center to one of the foci is 4 and the distance from the center to one of the vertices is 5.

Find the value of length of minor axis using the formula.

b2=a2-c2b2=25-16b2=9b=3

Thus, the equation of ellipse is as follows,

x2a2+y2b2=1x225+y29=1

On plotting the vertices and foci on the graph, we get,

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Most popular questions from this chapter

Graph each function.

f(x)=9-9x2.

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

A)y2=4xC)y2=-4xE)(y-1)2=4(x-1)G)(y-1)2=-4(x-1)B)x2=4yD)x2=-4yF)(x+1)2=4(y+1)H)(x+1)2=4(y+1)

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=8x

In Problems 43鈥�52, identify the graph of each equation without applying a rotation of axes.

3x2-2xy+y2+4x+2y-1=0
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