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Chapter 10: Q. 37 (page 654)

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

Center at(0,0), vertex at(0,4),b=1

Short Answer

Expert verified

The equation of ellipse is x2+y216=1and the graph is

Step by step solution

01

Step 1. Given Information

We are given vertex at(0,4),b=1

02

Step 2. Calculation

The vertices lie on the y-axis. So, the major axis of the ellipse is y-axis and the vertices formed by minor axis are (1,0)and(-1,0)

Find the value of foci using the formula.

b2=a2-c212=42-c2c2=16-1c2=15

Thus, the equation of ellipse is as follows,

x2b2+y2a2=1x212+y242=1x2+y216=1

On plotting the points on the graph, we get,

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