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Chapter 10: Q. 35 (page 654)

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

Foci at(0,卤3), x-intercepts are卤2

Short Answer

Expert verified

The equation of ellipse is x24+y213=1and the graph is

Step by step solution

01

Step 1. Given Information

We are given foci and x-intercept as(0,卤3);卤2respectively.

02

Step 2. Calculation

The center is at the midpoint of foci which is the origin. The major axis of the ellipse is the y-axis and the distance between the given x-intercept is less than the distance between the foci.

The x-intercepts of the ellipse are (b,0)and(-b,0). So, b=卤2and since one of the foci is (0,3). So, c=3

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

b2=a2-c24=a2-9a2=13

Thus, the equation of ellipse is as follows,

x2b2+y2a2=1x24+y213=1

On plotting the points on the graph, we get,

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