Question

If you are good with directrix ill give medal

Answer 1

@IMStuck sorry haha theres this one too

Answer 2

@niksva @SolomonZelman

Answer 3

Have you tried anything with this problem so far? Or not sure where to start?

Answer 4

i don't know where to start... im very good with parabolas but not when it comes to this stuff if that makes sense

Answer 5

If you are given two points, focus \((x_1, y_1)\) and directrix \((x_2, y_2)\) you can insert them in to this formula:

\((x - x_1)^2 + (y - y_1)^2 = (x - x_2)^2 + (y - y_2)^2\)

Answer 6

i only have one set of points so how would i do x2?

Answer 7

In this case, you have focus \((4,0)\) and directrix \((x, 10)\)

Answer 8

The directrix is \((x, 10)\) because y = 10 for any given x values.

Answer 9

ok so (x-4)^2+(y-0)^2=(x-x)^2+(y-10)^2?

Answer 10

After you insert the values in to the formula, you'll have

\((x - 4)^2 + (y - 0)^2 = (x - x)^2 + (y - 10)^2\)

Yes, exactly

Answer 11

square everything right?

Answer 12

Only expand the binomials with y variables.

Answer 13

what do you mean?

Answer 14

Leave \((x - 4)^2\) as is

Answer 15

oh so (x-4)^2+y^2=(x-x)^2+y^2-100?

Answer 16

\((x - 4)^2 + y^2 = (0)^2 + y^2 - 20y - 100\)

Remember:
\((x - x)^2 = (0)^2 = 0\)
\((y - 10)^2 = (y - 10)(y - 10)\)
\( = y(y - 10) - 10(y - 10)\\ = y^2 - 10y - 10y + 100 \\ = y^2 - 20y + 100 \)

Answer 17

then what?

Answer 18

Then solve for y