Question 329446: What is the equation of a parabola with a focus (10,6) and directrix y=4? Please show me how you get the answer. Answer by galactus(183) (Show Source):
You can put this solution on YOUR website! When a parabola as its axis parallel to the y-axis and is concave up, it has equation
where (h,k) are the vertex coordinates.
p is the distance from the vertex to the focus or from the vertex to the directrix. Thus, the distance from the focus to the directrix is 2p.
Since the y-coordinate of the focus is 6 and the directrix is at y=4, the distance between the focus and directrix is 2 units. This means 2p=2,
p=1
So, the focus coordinates (the h,k in the formula) are (10,5)
So, we have
is the parabola equation
