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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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