## anonymous one year ago What is the equation of the ellipse with co-vertices (0, 2), (0, -2) and vertices (3, 0), (-3, 0)? Please help? I have nO IDEA how to do this!

1. UnkleRhaukus

hmmm, lets draw a graph, and plot those points

2. UnkleRhaukus

|dw:1439094439604:dw|

3. UnkleRhaukus

|dw:1439094488079:dw| can you do the others?

4. UnkleRhaukus

(click on the yellow pencil icon, to reuse a drawing )

5. anonymous

|dw:1439094586269:dw| is this correct?

6. UnkleRhaukus

whoops, i plotted that first point wrong,

7. UnkleRhaukus

(my mistake) |dw:1439094795562:dw|

8. UnkleRhaukus

[that's better now (sorry about that)] now we have the co-vertices plotted, we can draw the ellipse , so that is goes through these points . . .

9. UnkleRhaukus

(can you draw the ellipse?)

10. anonymous

|dw:1439094980170:dw|

11. UnkleRhaukus

Good. |dw:1439095016485:dw|

12. UnkleRhaukus

Can you tell from the diagram now, where the centre of ellipse is ? and its semi-major axes?

13. anonymous

(0,0)

14. UnkleRhaukus

good, yes that is the centre

15. UnkleRhaukus

And remember that the axes are half the width (a), and half the height (b)

16. anonymous

it's 6, and 4, right?

17. UnkleRhaukus

the major axes (full width/height) are 6 and 4 we want the semi-major axes ... half these

18. anonymous

3, and 2

19. UnkleRhaukus

you now have $$(h,k)=(0,0)$$ $$a=3$$, $$b =2$$ so plug these into $\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2} = 1$

20. UnkleRhaukus

What do you get:

21. anonymous

(|dw:1439095772471:dw|

22. UnkleRhaukus

very good, now just simplify

23. anonymous

|dw:1439095814555:dw|

24. anonymous

y^2

25. UnkleRhaukus

|dw:1439095846244:dw|

26. UnkleRhaukus

Great work! you're done

27. anonymous

Thank you once again! :)