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Use Cartesian coordinates to express the equations for the ellipses determined by the conditions specified in Exercises 32–37.

foci(0,±α), minor axis2α

Short Answer

Expert verified

The answer isx2α2+y22α2=1.

Step by step solution

01

Step 1. Given information.

The given values are,

foci(0,±α), minor axis2α.

02

Step 2. values of the variables.

The foci are (0,α)(0,-α)

Centre=0+02,α-α2since mid point=x1+x22,y1+y22=(0,0)

Given minor axis is2α.Then2b=2αb=αc=(0-0)2+(0-α)2sinceD=x2-x12+y2-y12That is the distance from(0,α)(0,0).c=αNow takec2=a2-b2c2=a2-b2α2=a2-α2a2=2α2

03

Step 3. Substitution.

On substituting,

(x-h)2b2+(y-k)2a2=1wherea>b,(h,k)Is the center.(x-0)2α2+(y-0)22α2=1x2α2+y22α2=1.

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