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Chapter 10: Q. 43 (page 655)

Analyze each equation; that is, find the center, foci, and vertices of each ellipse. Graph each equation by hand. Verify your graph using a graphing utility.

(x-3)24+(y+1)29=1

Short Answer

Expert verified

The center of ellipse is (3,-1), foci are (3,-1+5)or(3,-1-5)and vertices formed by major axis are (3,2)or(3,-4).

The required graph is

Step by step solution

01

Step 1. Given Information 

The given equation is(x-3)24+(y+1)29=1

02

Step 2. Calculation  

The large number 9 is in the denominator of the term containing y2. So, ellipse has center at the origin and major axis parallel to y-axis.

Rewrite the given equation in the general form,

(x-3)222+(y-(-1))232=1

The center of ellipse is the point (h,k)=(3,-1). From the equation, we have b=2and distance from center to one of the vertex as 3.

Find the distance from center to foci using the formula,

c2=32-22c2=9-4c2=5c=5

Thus, the foci are as follows,

(h,k卤c)=(3,-1卤5)

The vertices formed by major axis are as follows,

(h,k卤a)=(3,-1卤3)

And the vertices formed by minor axis are(h卤b,k)=3卤2,-1

03

Step 3. Graph

Plot all the obtained points to get the required graph.

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Most popular questions from this chapter

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)

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

3x2+2xy+y2+4x-2y+10=0

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

Focus is at0,-3and vertex at0,0.

In Problems 15鈥�18, the graph of a hyperbola is given. Match each graph to its equation.

Equations:

Ax24-y2=1Bx2-y24=1Cy24-x2=1Dy2-x24=1

Graph:

The point that is symmetric with respect to the x-axis to the point (-2, 5) is ________.
See all solutions

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