## anonymous one year ago Find the standard form of the equation of the parabola with a focus at (-4, 0) and a directrix at x = 4.

1. misty1212

|dw:1440121717847:dw|

2. misty1212

HJI!!

3. misty1212

you need the vertex first, also which way it is oriented then it is quite quick do you know the vertex?

4. anonymous

0,0?

5. misty1212

yes !

6. misty1212

and how is it oriented? |dw:1440121829542:dw|

7. anonymous

first?

8. misty1212

yes again

9. misty1212

|dw:1440121936412:dw|

10. misty1212

because it opens to the left, that means the $$y$$ term is squared, and it will look like $y^2=px$

11. misty1212

all you need is $$p$$ the distance from the vertex to the focus, or from the directrix to the vertex what is that distance?

12. misty1212

oops i made a typo $y^2=4px$ is what i meant

13. anonymous

p=4

14. misty1212

ok so final answer $y^2=-16x$

15. misty1212

minus because it opens to the left

16. anonymous

oh okay so you just have to look for each part and then put it together THANK YOU SO MUCH!!

17. misty1212

right want to check the answer?

18. misty1212

$\color\magenta\heartsuit$ http://www.wolframalpha.com/input/?i=parabola+y%5E2%3D-16x

19. anonymous

y = negative one divided by sixteenx2

20. misty1212

oh no!

21. misty1212

the y term is squared, not the x term

22. anonymous

ohh yeah sorry haha

23. misty1212

if $y^2=-16x$ is not an "answer choice" try $x=-\frac{1}{16}y^2$

24. anonymous

could we do another one like this and you help me the same way?

25. misty1212

kk

26. anonymous

Find the standard form of the equation of the parabola with a focus at (0, -9) and a directrix y = 9.

27. misty1212

|dw:1440122328669:dw|

28. misty1212

vertex?

29. anonymous

so it open down? vertex is 0,0

30. misty1212

yeah opens down so the x term is squared and its coefficient it negative

31. misty1212

distance is clear right?

32. anonymous

p=9

33. misty1212

right so $x^2=-36y$ should do it

34. anonymous

wait how did 36 come from 9

35. misty1212

$4\times 9$

36. misty1212

$x^2=4py$

37. anonymous

ohhh yeah okay haah and wouldn't it be y=-1/36x2

38. misty1212

that too

39. anonymous

oh okay

40. anonymous

thank you so much! If I have any more tonight ill tag you in them :)

41. misty1212

$\huge\color\magenta\heartsuit$