Which of the following is an equation of an ellipse centered at the origin and with axial intersections at `(0, pm3)` and `(pm 2, 0)` ?

Options

A. `(x)/(2)+(y)/(3)=1`
B. `(x)/(2)+(y)/(3)=2`
C. `(x)/(3)+(y)/(2)=2`
D. `(x^(2))/(4)+(y^(2))/(9)=1`

Answer

D

Explanation

When an ellipse is centreed at the origin and has major and minor axes along the x - and y - axes, the equation of the ellipse is
`(x^(2))/(a^(2))+(y^(2))/(b^(2))=1`
Where the axial intersections are `(pm a, 0)` and `(0, pm b)`. In Example `6, a = 2` and b = 3, so the equation is

`(x^(2))/(2^(2))+(y^(2))/(3^(2))=1`
`(x^(2))/(4)+(y^(2))/(9)=1`
Note that if you don't remember the formula, you can still find the answer. It just takes a little longer. You have four points whose coordinates will satisfy the correct equation : (0,3), (0, -3), (2, 0), and (-2, 0). The only choice that works with all of these points is (D).
Every once in a while, a hyperbola turns up on the Math 2 test. Here's an equation of a hyperbola. It looks a lot like the equation for an ellipse, except that there's a minus sign.
`(x^(2))/(a^(2))-(y^(2))/(b^(2))=1`
You've covered the coordinate geometry topics that you're likely to encounter on the Math 2 test. You've reviewed the facts and formulas and learned some useful strategies. You may also see a question on one of the following.