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

1. anonymous

2. UnkleRhaukus

looks like an ellipse, where is it centred? what are the semimajor axes?

3. anonymous

it is, and isn't it centered at (0,0)? and I don't know them..

4. UnkleRhaukus

yes it is centred at the origin: (0,0)

5. UnkleRhaukus

Semi major axes of an ellipse look like this |dw:1439092799738:dw|

6. anonymous

|dw:1439092817312:dw| we have to use this equation, correct?

7. UnkleRhaukus

A general form of an ellipse centred at the point $$(h,k)$$, with semi major axes $$a$$, and $$b$$, (in the x and y directions respectively ) is $\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2} = 1$

8. UnkleRhaukus

yeah we have the centre $$(h,k)$$ = $$(0,0)$$ so it reduces to $\frac{x^2}{a^2}+\frac{y^2}{b^2} = 1$

9. UnkleRhaukus

we just need to get $$a$$, (half the width) and $$b$$, (half the height)

10. anonymous

how do we get that?

11. UnkleRhaukus

look at the diagram,

12. UnkleRhaukus

|dw:1439093170591:dw|

13. anonymous

so then A would be 1.5, and B would be 3 ?

14. UnkleRhaukus

not quite, the full width of the ellipse is 3 - (-3) = 6 the full height of the ellipse is 6 - (-6) = 12 so half the width is 6/2 = ... and the half height is 12/2 = ......

15. anonymous

3, and 6, or is it in that fraction form?

16. UnkleRhaukus

thats right the semi-major axis (in the x direction) : a = 3 and the semi-major axis in the y direction: b = 6

17. UnkleRhaukus

So what does the equation of our ellipse look like now?

18. anonymous

|dw:1439093577574:dw|

19. UnkleRhaukus

goood, now just simplify 3^2 and simplify 6^2

20. anonymous

9 & 36

21. UnkleRhaukus

Cool, so your equation is $\frac{x^2}9+\frac{y^2}{36} = 1$ A further step to make the final equation a little nicer could be to multiply both sides by 9 $x^2+\frac{y^2}{4} = 9$ but you might prefer to keep it as $$\frac{x^2}9+\frac{y^2}{36} = 1$$

22. anonymous

Thank you! :)

23. UnkleRhaukus

i suppose another option for a nice final form might be $\left(\frac x3\right)^2+\left(\frac y6\right)^2=1$ They all kinda look nice.