## anonymous one year ago PLEASE HELP ME WRITE THE EQUATION FOR AN ELLIPSE: (MEDAL AND FAN!!!): Write the equation of an ellipse with center (2,1); vertex (7,1) ; and focus (5,1).

1. ganeshie8

|dw:1439810883867:dw|

2. anonymous

Ok that makes sense, so how do I get a? I am just confused sorry.

3. ganeshie8

|dw:1439810946525:dw|

4. ganeshie8

so it seems it is going to be a horizontal ellipse ?

5. anonymous

Yes

6. anonymous

I know that the equation is going to look like this: $\frac{ (x-2)^2 }{ ? } + \frac{ (y-1)^2 }{ ? } = 1$

7. ganeshie8

Right, center = $$(h,k)=(2,1)$$ we need to find the values of $$a,b$$ and plug in : $\dfrac{(x-2)^2}{a^2}+\dfrac{(y-1)^2}{b^2}=1$

8. anonymous

I just need a^2 and b^2...

9. ganeshie8

use the vertex formula : $$(h+a, k)=(7,1)$$ can you find the value of $$a$$ ?

10. anonymous

is it 5?

11. ganeshie8

Correct. $$2+a=7\implies a=5$$

12. anonymous

ok and then b?

13. ganeshie8

Next use focus formula $$(h+c,~k)=(5,1)$$ can you find the value of $$c$$ ?

14. anonymous

Is it 2?

15. ganeshie8

nope

16. anonymous

Not sure, sorry

17. ganeshie8

$$h+c=5$$ you know that $$h=2$$, therefore $$c=?$$

18. anonymous

3?

19. ganeshie8

Yes, $$a=5,~c=3$$ we still need to find $$b$$

20. anonymous

ok so I use this right: c^2 = b^2 - a^2?

21. ganeshie8

it should be $$a^2 = b^2+c^2$$

22. anonymous

whoops ok, sorry: 5^2 = 3^2 + b^2 25 = 9 + b^2 16 = b^2 b = 4

23. ganeshie8

Excellent!

24. anonymous

Ok so my final answer is: $\frac{ (x-2)^2}{ 25 } + \frac{ (y-2)^2 }{ }$

25. anonymous

whoops i messed that up under the (y-2)^2 is 16. and it all equals 1 right?

26. anonymous

Ok so now that i got that, how do I approach this when I am given center, co-vertex, and focus? Can i post the question?

27. ganeshie8

Ok so my final answer is: $\frac{ (x-2)^2}{ 25 } + \frac{ (y-\color{red}{1})^2 }{ \color{red}{16} }$

28. anonymous

Sorry that is what i meant, lol i had that written down...