Question

Which of the following equations is of an ellipse with x-intercepts of (3, 0) and (-3, 0) and y-intercepts at (0, 1) and (0, -1)?

Answer 1

The equation of ellipse is
`(x^(2) )/(9)+(y^(2) )/(1)=1`

Explanation:

Given: An ellipse has

x-intercepts are (-3,0) and (3,0)

y-intercepts are (0,-1) and (0,1)

Let,

Length of major axis of ellipse is 2a and minor axis as 2b

Now,

The distance between two points is given by :

L=
`\sqrt{(X2-X1)^(2)+(Y2-Y1)^(2)}`

The distance between x-intercepts (-3,0) and (3,0) :

X=
`\sqrt{(X2-X1)^(2)+(Y2-Y1)^(2)}`

X=
`\sqrt{((-3)-3)^(2)+(0-0)^(2)}`

X=6

The distance between Y-intercepts (0,-1) and (0,1) :

Y=
`\sqrt{(X2-X1)^(2)+(Y2-Y1)^(2)}`

Y=
`\sqrt{(0-0)^(2)+((-1)-1)^(2)}`

Y=2

Since, X>Y

An ellipse is parallel to x-axis

2a=6 and 2b=2

a=3 and b=1

From the equation of ellipse ;

`(x^(2) )/(a^(2))+(y^(2) )/(b^(2))=1`

`(x^(2) )/(3^(2))+(y^(2) )/(1^(2))=1`

`(x^(2) )/(9)+(y^(2) )/(1)=1`