Asked by Hannah
What is the equation of the parabola, given the following equation:
Directrix is the y-axis and focus at (3,5)
Directrix is the y-axis and focus at (3,5)
Answers
Answered by
Reiny
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,
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,
Answered by
oobleck
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.
Answered by
Hannah
I now get it. Thank you very much!
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.