Question

Which equation represents a parabola that has a focus of (0, 0) and a directrix of y = 2?

x2=−4(y−1)

x2=−4y

x2=−y

x2=−(y−1)

Answer 1

@Hero

Answer 2

One moment while I switch from tablet tablet to laptop

Answer 3

...

Answer 4

Sorry for taking so long. I just got off from work. You caught me in a transition stage.

Answer 5

Anyway you can use the distance formula to find the equation of the parabola.

Answer 6

The distance formula for finding the equation of a parabola is
\[(x - x_1)^2 + (y - y_1)^2 = (x - x_2)^2 + (y - y_2)^2\]

Where the focus is \((x_1, y_1) = (0,0)\) and the directrix is \((x_2, y_2) = (x, 2)\)

Answer 7

Notice that plugging the appropriate points in to the formula yields:
\((x - 0)^2 + (y - 0)^2 = (x - x)^2 + (y - 2)^2\)

@princeevee would you mind attempting to simplify the above?

Answer 8

hmmm...

Answer 9

(X)^2 + x^2 + y^2?

Answer 10

Not quite. Let's take it one step at a time. What does \((x - 0)^2\) simplify to?

Answer 11

@princeevee are you there?

Answer 12

sorry, connection machine broke

Answer 13

Is it fixed now?

Answer 14

When you simplify the equation after inputting the values, you should have ended up with \(x^2 + y^2 = (y - 2)^2\)

The next step is to expand the \((y - 2)^2\) on the right side of the equation.

Answer 15

crap....

Answer 16

@princeevee are you able to expand \((y - 2)^2\) ?

Answer 17

its kinda a bit difficult for me...can you do it?

Answer 18

@Ultrilliam

Answer 19

just for some extra help

Answer 20

I'll show you how to expand \((y - 3)^2\):

\begin{align*}(y - 3)^2 &= (y - 3)(y - 3) \\&=y(y - 3) - 3(y - 3) \\&=y^2 -3y -
3y + 9 \\&=y^2 - 6y + 9\end{align*}