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Chapter 10: Q. 34 (page 654)

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

Focus at0,-4, vertices at0,卤8

Short Answer

Expert verified

The equation of ellipse is x248+y264=1and the graph is

Step by step solution

01

Step 1. Given Information

We are given Focus and vertices as0,-4and(0,卤8)respectively.

02

Step 2. Calculation

Since the given vertices and focus lies on the y-axis then the y-axis is the major axis. The center is the midpoint of the vertices

The distance from the center to one of the foci is 4 and the distance from the center to one of the vertices is 8.

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

b2=a2-c2b2=64-16b2=48

Thus, the equation of ellipse is as follows,

x2a2+y2b2=1x248+y264=1

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

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Most popular questions from this chapter

Find the intercepts of the equation y2=16-4x2.

The graph of a parabola is given. Match 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 an equation for each ellipse. Graph the equation by hand.

Center at(1,2)vertex at(1,4) contains the point(1+3,3).

Find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation by hand.

Focus is at-4,0and vertex is at0,0.

Graph each function.

f(x)=-64-16x2
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