Answer:
The equation of ellipse is [tex]\frac{x^{2} }{9}+\frac{y^{2} }{1}=1[/tex]
Step-by-step 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=[tex]\sqrt{(X2-X1)^{2}+(Y2-Y1)^{2}}[/tex]
The distance between x-intercepts (-3,0) and (3,0) :
X=[tex]\sqrt{(X2-X1)^{2}+(Y2-Y1)^{2}}[/tex]
X=[tex]\sqrt{((-3)-3)^{2}+(0-0)^{2}}[/tex]
X=6
The distance between Y-intercepts (0,-1) and (0,1) :
Y=[tex]\sqrt{(X2-X1)^{2}+(Y2-Y1)^{2}}[/tex]
Y=[tex]\sqrt{(0-0)^{2}+((-1)-1)^{2}}[/tex]
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 ;
[tex]\frac{x^{2} }{a^{2}}+\frac{y^{2} }{b^{2}}=1[/tex]
[tex]\frac{x^{2} }{3^{2}}+\frac{y^{2} }{1^{2}}=1[/tex]
[tex]\frac{x^{2} }{9}+\frac{y^{2} }{1}=1[/tex]
