The definition of a parabola:
The set of points which are equidistant from a given focus and a given directrix.
Let one such point be (x,y)
so √( (x-0)^2 + (y-y)^2 ) = √( (x-3)^2 + (y-5)^2)
square both sides and simplify
x^2 = x^2 - 6x + 9 + y^2 - 10y + 25
6x = y^2 - 10y + 34
x = (1/6)(y^2 - 10y + 34)
check my arithmetic,
What is the equation of the parabola, given the following equation:
Directrix is the y-axis and focus at (3,5)
3 answers
Recall that the parabola y^2 = 4px has
focus at (p,0)
directrix x = -p
vertex at (0,0)
Note that the vertex is midway between the focus and the directrix.
So, your parabola has vertex at (3/2,5)
p = 3/2
So, (y - 5)^2 = 4(3/2)(x - 3/2)
as Reiny derived above.
focus at (p,0)
directrix x = -p
vertex at (0,0)
Note that the vertex is midway between the focus and the directrix.
So, your parabola has vertex at (3/2,5)
p = 3/2
So, (y - 5)^2 = 4(3/2)(x - 3/2)
as Reiny derived above.
I now get it. Thank you very much!
1 answer