Question

What is the equation of the parabola with focus (1,0) and directrix y=4

Answer 1

Given:

Focus = (1,0)

Directrix=y=4

To determine the equation of the parabola, we first find the middle distance between the focus and the directrix:

Middle distance= 4/2=2

Based on the given middle distance, the vertex would be:

`(h,k)=(1,0+2)=(1,2)`

Next, we use the formula:

`(x-h)^2=4p(y-k)`

where:

h=1

k=2

p=distance between the focus and vertex=2

So,