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Chapter 10: Q. 32 (page 654)

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

Foci at0,卤2, length of major axis is 8

Short Answer

Expert verified

The equation of ellipse is x212+y216=1and the graph is

Step by step solution

01

Step 1. Given Information

The given data is Foci at 0,卤2, length of major axis is 8

02

Step 2. Calculation

The ellipse has a center at the origin. Since focus lies on the y-axis then the y-axis is the major axis.

The distance from center to focus of the ellipse is 2 and given the length of major axis as2a=8鈬�a=4

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

b2=a2-c2b2=16-4b2=12

Thus, the equation of ellipse is as follows,

x2a2+y2b2=1x212+y216=1

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

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Most popular questions from this chapter

In Problems 31鈥� 42, rotate the axes so that the new equation contains no xy-term. Analyze and graph the new equation. Refer to Problems 21鈥�30 for Problems 31鈥� 40.

5x2+6xy+5y2-8=0

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

Foci at(1,2)and(-3,2): vertex at(-4,2).

Answer Problem using the figure.

If a = 4, then the coordinates of the focus are___________.

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

Center at (-3,1): vertex at (-3,3): focus at(-3,0)

True or False

The equation 3x2+Bxy+12y2=10defines a parabola ifB=-12.
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