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 $\frac{ x^{2} }{b^2} + \frac{y^2}{a^2}=1$.  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 $\frac{x^2}{1}+ \frac{y^2}{9}=1$, choice a from above.