Find k for Ellipse with Major Axis Length 6 | Exam Study Help

[petuniac]

ellipse - urgent help needed

Hi there.. i have an exam tomorrow morning and can't figure this out.

ellipse defined by 3x^2 + 2y^2 = k
length of major axis is 6
find k?

ok.. i know that the major axis = 2a, so in this case a = 3
the general form of an ellipse is

x^2/a^2 + y^2/b^2 = 1

? where do i go now ?

 

[Ateowa]

So the equation for the ellipse is 3x² + 2y²=k. The length of the major axis let's you fill in the following into the ellipse equation: x²/9 + y²/b^2=1. The 9 allows you to finish the problem. Do you remember how you bring an ellipse from the general form to the standard form for an ellipse?

Let's pretend that we're trying to take the original equation to standard form for an ellipse. You want the right side of the equation to equal 1, so you divide by k. That means that the standard form, in this case, would be 3x²/k + 2y²/k=1. But you always have to simplify. The coefficient of x must be gone in the final equation, so that means that the a² must have been simplified. With that information, you should be able to take the jump to find k (That is, if I worded it right =) ).