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Chapter 9: Q. 34 (page 772)

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

foci(3,卤5), major axis12

Short Answer

Expert verified

The equation isy236+(x-3)211=1.

Step by step solution

01

Step 1. Given information.

It is given,

foci(3,卤5), major axis12

02

Step 2. Value of the variables.

Focus points are (3,5)(3,-5).

center=3+32,5-52=(3,0)

Givenmajoraxisis122b=12b=6c=(3-3)2+(0-5)2sinceD=x2-x12+y2-y12That is the distance from(3,5)(3,0).c=5Now,c2=b2-a252=62-a225=36-a2a2=11

03

Step 3. Substitution.

On substituting the obtained values in,

(y-k)2b2+(x-h)2a2=1whereb>a,(h,k)is the center.(y-0)236+(x-3)211=1y236+(x-3)211=1

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