anonymous one year ago 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?

1. anonymous

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

2. anonymous

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

3. anonymous

No I don't

4. anonymous

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

5. anonymous

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 $$b$$

6. anonymous

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

7. anonymous

could be let me check

8. anonymous

no but you have the right idea

9. anonymous

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

10. anonymous

first off "horizontal minor axis" is shorter than the "vertical major axis" that means it looks like this |dw:1439255560209:dw|

11. anonymous

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

12. anonymous

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

13. anonymous

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

14. anonymous
15. anonymous

again the larger number should be under the $$y$$ term since the major axis is vertical

16. anonymous

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