Question

Derive the equation of the parabola with a focus at (−2, 4) and a directrix of y = 6. Put the equation in standard form.

Answer 1

If you are given the focus \((x_1, y_1)\) and directrix \((x_2, y_2)\) of a parabola, then you can insert those points in to the distance formula:
\((x - x_1)^2 + (y - y_1)^2 = (x - x_2)^2 + (y - y_2)^2 \). Then simplify and solve for y to find the standard form of the parabola.

Answer 2

im so confused

Answer 3

You are basically given two points:

Focus:
\((x_1, y_1) = (-2, 4)\)

Directrix
\((x_2, y_2) = (x,6)\)

Insert the points into the formula then simplify and isolate y. Try to think about what should be done first. You can ask questions if you're confused about anything.

Answer 4

yea but what is the directrix? like what do i put for that ?

Answer 5

The directrix is a horizontal line y = 6. When you express that line as a point it becomes \((x, 6)\). What that means is, no matter the value of x, y will always be 6 at every point on the line.

Answer 6

Basically, it's just a matter of inserting the points into the formula and then simplifying. Have you tried inserting the points? Insert what you can and then post what you've done so far here.

Answer 7

i tried but when it says y-y2 what do i put for that ?

Answer 8

Please post everything you inserted for the entire formula. We'll go over anything you're stuck on afterwards. You can use the draw button to post your steps if you want.