## anonymous one year ago Hey, I need help with one question about ellipses. I have to go so a simple step by step for the situation and then with my numbers to plug in would be good. Please help quickly... The question is: Write the equation of an ellipse with center (-3,2); covertex (-8,2) and focus (-3,-10)

1. Loser66

What is the formula of a shifted ellipse?

2. anonymous

$\frac{ (x-h)^2 }{ a^2 } + \frac{ (y-k)^2 }{ b^2 } = 1$?

3. Loser66

Yup!! how to find the major vertices from foci and co-vertices?

4. Loser66

c^2=......

5. anonymous

c^2 = a^2 - b^2

6. Loser66

Yes, you have foci c, and b, how to find a^2?

7. anonymous

what what is c? is it -3?

8. anonymous

sorry you kind of lost me...

9. Loser66

no no, I am just asking about the formula, not number yet.

10. anonymous

oh ok. I think to find a^2 you turn it around so it is: a^2 = b^2 = c^2? or is it a completely different formula

11. Loser66

ok, now, draw out the given points.

12. anonymous

|dw:1439814717542:dw|

13. Loser66

|dw:1439814693102:dw|

14. anonymous

5 units

15. Loser66

yes, so from the center, go to the right 5 units, what is the other co-vertex?

16. anonymous

2,2?

17. Loser66

yes, again

18. Loser66

|dw:1439814820325:dw|

19. anonymous

8 units

20. Loser66

nope

21. anonymous

oh lol 12 sorry i wasn't thinking

22. Loser66

ok, that is c, and b is 5 hence a^2=?

23. anonymous

a^2 = 5^2 + 12^2 a^2 = 25 + 144 a^2 = 169

24. Loser66

ok, a =?

25. anonymous

13

26. Loser66

plug them into the standard equation.

27. anonymous

I get this: $\frac{ (x+3)^2 }{ 25 } + \frac{ (y-2)^2 }{ 169 } = 1$

28. anonymous

is that right?

29. misty1212

looks good to me!