Question

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

a.) x^2/1 + y^2/9 =1
b.) x^2/1 - y^2/9 =1
c.) x^2/9 + y^2/1 =1

Answer 1

If you were to plot the x and y intercepts you would see that this will be a vertical ellipses, taller that it is wider. The formula for an ellipse is
`( x^(2) )/(b^2) + (y^2)/(a^2)=1`. The "a" value is always the bigger value of the a and b. The bigger value, the a, will always go under the variable that is the major axis. The major axis for us is the y axis. a = 3, so 3 squared is 9. b = 1 and 1 squared is 1. So our equation will be
`(x^2)/(1)+ (y^2)/(9)=1`, choice a from above.