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Chapter 10: Q 61. (page 655)

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

Center at (1,2): focus at (4,2): contains the point(1,3)

Short Answer

Expert verified

The equation of the ellipse is (x-1)210+(y-2)2=1and graph of the ellipse is

Step by step solution

01

. Given information.

Center at (1,2): focus at (4,2): contains the point (1,3)

By using distance formula the value of ais

a=(4-1)2+(2-3)2a=9+1a=10

Since a=10and the major axis is parallel to the x-axis, the vertices are 10units to the left and right of the center.

Thus, the vertices are v1=(1+10,2)and v2=(1-10,2).

The distance between the center and the focus will give the value of c.

c=(4-1)2+(2-2)2c=9c=3

02

Step 2. The equation of ellipse.  

Substituting c=3and a=10we get.

localid="1646723555627" b2=(10)2-(3)2b2=10-9b2=1

The equation of the ellipse is(x-1)210+(y-2)2=1

03

.Graph of the ellipse .   

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Most popular questions from this chapter

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

Center at (2,-2): vertex at (7,-2): focus at(4,-2).

The graph of a parabola is given. Match each 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)

In Problems 43鈥�52, identify the graph of each equation without applying a rotation of axes.

4x2+12xy+9y2-x-y=0

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.

localid="1647365908255" x2+4xy+y2-3=0

The graph of a parabola is given. Match each graph to its equation.
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