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Chapter 9: Q. 32 (page 772)

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

foci(卤1,0),major axis4

Short Answer

Expert verified

The equation isx24+y23=1.

Step by step solution

01

Step 1. Given information.

We are given,

foci(卤1,0),major axis4

02

Step 2. Value of the variables.

The focus points are (1,0)(-1,0).

The center which is the midpoint of the focus points is,

=1-12,0since mid point=x1+x22,y1+y22=(0,0)Given major axis is4.Then2a=4a=2Now,c=(1+0)2+(0-0)2sinceD=x2-x12+y2-y12c=1Now,Again,c2=a2-b21=4-b2b2=3

03

Step 3. Substitution.

On substituting the obtained values,

(x-h)2a2+(y-k)2b2=1wherea>b,(h,k)is the center.(x-0)24+(y-0)23=1x24+y23=1

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Most popular questions from this chapter

Consider the hyperbola with equation x2A2-y2B2=1.Let F be the focus with coordinates (A2+B2,0).Let e=A2+B2A and l be the vertical line with equation x=Ae. Show that for any point P on the hyperbola, FPDP=e,where D is the point on l closest to P.

Show that the eccentricity satisfies the equationB2=A21-e2.

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

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