Question

What is the equation of an ellipse centered at (5,-1) having a horizontal minor axis of length 4 and a major axis of length 6?

Answer 1

do you know the general form of an ellipse with center \((h,k)\)?

Answer 2

just asking is all
if the answer is "NO" i will show you

Answer 3

No I don't

Answer 4

no one likes these conic section problems but they are not that hard

Answer 5

general form of ellipse with center \((h,k)\) is
\[\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1\]
you are already given \((h,k)\) all you need now is \(a\) and \(b\)

Answer 6

(x-5)^2/36+(y-1)^2/16=1 was the equation I got is this correct ?

Answer 7

could be let me check

Answer 8

no but you have the right idea

Answer 9

Or was is suppose to be (x+5)^2/9+(y+1)^2/4=1 ?

Answer 10

first off "horizontal minor axis" is shorter than the "vertical major axis"
that means it looks like this

Answer 11

second answer is even closer, you got the deominators right, but they are backwards

Answer 12

half of 6 is 3 and \(3^2=9\) likewise \(2^2=4\) but since it is oriented the other way, the larger number should be under the \(y\) term not the x terms

Answer 13

So (x-5)^2/9+(y-1)^2/4=1?

Answer 14

looks like this
http://www.wolframalpha.com/input/?i=ellipse+%28x-5%29^2%2F4%2B%28y%2B1%29^2%2F9%3D1

Answer 15

again the larger number should be under the \(y\) term since the major axis is vertical

Answer 16

\[\frac{(x-5)^2}{4}+\frac{(y+1)^2}{9}=1\]