## anonymous one year ago What is the equation of the following graph?

1. anonymous

@Michele_Laino

2. Michele_Laino

that is a traslated ellipse

3. Michele_Laino

as you can see from the graph, the center of our ellipse is located at (0,-2)

4. anonymous

y2/9+x2/1

5. Michele_Laino

no, since we have to make a traslation

6. Michele_Laino

let's consider a new coordinate system X,Y located at point (0,2), namely at the center of your ellipse

7. Michele_Laino

with respect to the XY system the equation of our ellipse is: $\Large \frac{{{X^2}}}{1} + \frac{{{Y^2}}}{9} = 1$

8. Michele_Laino

am I right?

9. anonymous

yes

10. Michele_Laino

here is the situation of your exercise: |dw:1439652920237:dw|

11. Michele_Laino

oops.. I made a typo, the center of our ellipse is located at poin (0,-2)

12. Michele_Laino

and the equations of our traslation are: $\Large \left\{ \begin{gathered} x = X \hfill \\ y = Y - 2 \hfill \\ \end{gathered} \right.$

13. anonymous

okay

14. Michele_Laino

now, please solve that system for X, and Y, what do you get?

15. anonymous

im lost now.

16. Michele_Laino

hint: we have this: $\Large X = x$ right?

17. anonymous

yes

18. sohailiftikhar

what you want to know?

19. Michele_Laino

ok! now do the same, namely write Y as a function of y, please

20. anonymous

y=y-2 ?

21. Michele_Laino

$\Large Y = y + 2$

22. anonymous

oh okay

23. Michele_Laino

next, replace X with x, and Y with y+2 into my equation above

24. Michele_Laino

namely into this equation: $\Large \frac{{{X^2}}}{1} + \frac{{{Y^2}}}{9} = 1$ what equation do you get?

25. anonymous

idk im lost again..im glad im going over this other wise i would have gotten this wrong

26. Michele_Laino

hint: $\Large \frac{{{x^2}}}{1} + \frac{{{{\left( {y + 2} \right)}^2}}}{9} = 1$ is it right?

27. anonymous

yes

28. Michele_Laino

that is the requested equation

29. anonymous

so that the anwser?

30. Michele_Laino

yes!

31. Loser66

For shifted one, you need center (h, k), the way to find out a, b as what we had done before. The way a goes with major axis is the same. Just the numerators change to (x-h) ^2 and (y-k)^2. Dat sit.