Question

Derive the equation of the parabola with a focus at (2, 4) and a directrix of y = 8.

f(x) = −one eighth (x − 2)2 + 6
f(x) = one eighth (x − 2)2 + 6
f(x) = −one eighth (x + 2)2 + 8
f(x) = one eighth (x + 2)2 + 8

Answer 1

I know its negative, leaving options A and C

Answer 2

@SolomonZelman

Answer 3

@MilkNCookies

Answer 4

@ParthKohli

Answer 5

@Owlcoffee

Answer 6

@mathmale

Answer 7

How would the parabola look like? Upward or downward?

Answer 8

downward

Answer 9

im not sure how to do that

Answer 10

Step 3: Set the equation of the distance between P to Focus equal to the distance between P to directrix.

Makes sense?

Answer 11

yes

Answer 12

Correct. Do you have any idea on how to find the vertex from a given directrix and focus?
We know that the vertex is between the directrix and the focus.
To find the vertex:
Let the distance from point (x,y) to focus (2,4) equal to the distance of point (x,y) to the directrix
Here are the steps:
Step 1: Find the distance between the P (point) from the focus (2,4). P is a point (x,y) ( we don't know it).
\(\sqrt{(x - 2)² + (y - 4)²}\)