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Chapter 10: Q. 31 (page 654)

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

Foci at ±2,0, length of major axis is 6

Short Answer

Expert verified

The equation of ellipse is x29+y25=1and graph is

Step by step solution

01

Step 1. Given Information

The given data is Foci at ±2,0, length of major axis is 6

02

Step 2. Calculation

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

The distance from center to focus of the ellipse is c=2and given the length of major axis as 2a=6⇒a=3

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

b2=a2-c2b2=32-22b2=9-4b2=5b=±5

Thus, the equation of ellipse is as follows,

x2a2+y2b2=1x29+y25=1

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

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