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

Question

amistre64 · Answer

all points that are the same distance from the focus and the directrix .... equate the distances

anonymous · Answer

the distance from the focus to the directrix is 8

amistre64 · Answer

$$d_f^2=(x+4)^2+(y)^2$$
$$d_d^2=(x-4)^2+(y-y)^2$$

amistre64 · Answer

$$(x+4)^2 + y^2=(x-4)^2$$
$$x^2+8x+16 + y^2=x^2-8x+16$$
$$\cancel{x^2}+8x\cancel{+16} + y^2=\cancel{x^2}-8x\cancel{+16}$$
$$8x+y^2=-8x$$
etc....

anonymous · Answer

would this be the final answer

amistre64 · Answer

of course not ... hence the 'etc...'

anonymous · Answer

ok so I would have to divide by -8 on both sides

amistre64 · Answer

you could if you wanted to ... work out the steps and let me see what you come to

amistre64 · Answer

are we getting stuck in another site crash?

anonymous · Answer

8x+y^2=-8x
y^2=-1x

anonymous · Answer

idk

amistre64 · Answer

your thought was fine, your process if off

amistre64 · Answer

8x  +y^2 = -8x
/-8     /-8     /-8
---------------
-x - y^2/8 = x

might i suggest adding and x to both sides?

anonymous · Answer

y^2/8=x^2

amistre64 · Answer

a different approach would be to get the xs all to one side first

  8x+y^2=-8x 
-8x             -8x
--------------
      y^2 = -16x

then divide,  just less steps to take

amistre64 · Answer

-x - y^2/8 = x
+x              +x
--------------
     -y^2/8 = 2x
                    adding is not multiplication so no x^2

anonymous · Answer

thanks

amistre64 · Answer

i take it you got it from here?  good luck