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

Answer:

The equation of ellipse is $\frac{x^{2} }{9}+\frac{y^{2} }{1}=1$

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

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 ;

$\frac{x^{2} }{a^{2}}+\frac{y^{2} }{b^{2}}=1$

$\frac{x^{2} }{3^{2}}+\frac{y^{2} }{1^{2}}=1$

$\frac{x^{2} }{9}+\frac{y^{2} }{1}=1$