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Chapter 10: Q. 39 (page 654)

Write an equation for each ellipse.

Short Answer

Expert verified

The equation of ellipse is(x+1)24+(y-1)2=1

Step by step solution

01

Step 1. Given Information 

The given graph is

02

Step 2. Calculation 

The ellipse in the given graph has center at the point (-1,1)So, role="math" localid="1647278093172" h=-1,k=1From the graph, we can say that the center, focus and vertex of ellipse all lie on the same line y=1. So, major axis is parallel to x-axis.

The vertices of the major axis of the ellipse are at (h-a,k)=(-3,1)and(h+a,k)=(1,1)and vertices of the minor axis are at

(h,k-b)=(-1,0)and(h,k+b)=(-1,2)

Consider h+a=1andk+b=2. Since h=-1,k=1, the equations will be as follows,

-1+a=1a=2and1+b=2b=1

Thus, the equation of ellipse will be as follows,

(x-h)2a2+(y-k)2b2=1(x-(-1))222+(y-1)212=1(x+1)24+(y-1)2=1

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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)

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.

A(n)__________ is the collection of all points in the plane such that the distance from each point to a fixed point equals its distance to a fixed line.

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

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

Answer Problem using the figure.

If a = 4, then the equation of the directrix is______ .
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