- anonymous

Find the standard form of the equation of the parabola with a focus at (-8, 0) and a directrix at x = 8.

- chestercat

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- triciaal

|dw:1433220174652:dw|

- triciaal

@jim_thompson5910 please verify

- jim_thompson5910

The parabola will open to the left side, so it will have a y^2 term (instead of an x^2 term)

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## More answers

- triciaal

not use to those so the vertex is (0,0)

- jim_thompson5910

|dw:1433217367354:dw|

- jim_thompson5910

|dw:1433217380478:dw|

- jim_thompson5910

|dw:1433217399104:dw|

- jim_thompson5910

|dw:1433217436087:dw|

- jim_thompson5910

I'm using the ideas shown here
http://www.mathwords.com/f/focus_parabola.htm
4p(x-h) = (y-k)^2
4*8(x-0) = (y-0)^2
32x = y^2
x = (1/32)*y^2
x = -(1/32)*y^2 ... the coefficient is made to be negative so the parabola opens to the left (instead of right)
|dw:1433217556903:dw|

- triciaal

so is the equation I have wrong ?

- jim_thompson5910

anything with x^2, and not y^2, will open upward or downward

- triciaal

I actually have the same diagram see above (not as neat )

- jim_thompson5910

I see it, but again, you'll have y^2 instead of x^2

- jim_thompson5910

http://images.flatworldknowledge.com/reddenint/reddenint-fig08_009.png

- triciaal

|dw:1433221628889:dw|

- triciaal

you are saying since I have the directrix vertical instead of horizontal then the value from f to v is the y component?

- jim_thompson5910

because the directrix is vertical, this means that the parabola will open to the left or right
https://dr282zn36sxxg.cloudfront.net/datastreams/f-d%3A7980ac3c31917d6d9238e3fe5ee79be178774387290a21eba7ba82d2%2BIMAGE%2BIMAGE.1

- triciaal

got that not the problem
what I am missing is how to write the equation

- jim_thompson5910

http://www.mathwords.com/f/focus_parabola.htm
you use 4p(x-h) = (y-k)^2
since the parabola opens to the left, p < 0 based on that previous image. So p = -8
(h,k) = (0,0) is the vertex

- triciaal

@jim_thompson5910 thank you so much !!! I will look at the links guess better try to learn that version of the equation thank you

- anonymous

So what would the finally equation be?

- anonymous

*final

- anonymous

- triciaal

follow what Jim had above. I am used to the other format and in addition I had my x and y switched since it opened left, sorry

- jim_thompson5910

It depends on what format they want it in, but you could go with something in the form x = ay^2 + by + c

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