What is the equation in standard form of the parabola with a focus at (14,5)...
What is the equation in standard form of the parabola with a focus at (14,5) and a directrix of y=-15?
Answer & Explanation
Focus is at (14,5) and directrix is y=-15. Vertex is at midway
between focus and directrix. Therefore vertex is at
(14, ) or (14, -5). The vertex form of equation of
parabola is ; (h.k); being vertex. Here
h=14 and k=-5 So the equation of parabola is
. Distance of vertex from directrix is
d=15-5=10, we know or
. Here the directrix is below
the vertex , so parabola opens upward and a is positive.
Hence the equation of parabola is
the standard form of a parabola in translated form is.
where (h,k) are the coordinates of the vertex
and p is the distance from the vertex to the focus
since the directrix is below the focus then the curve
coordinates of vertex
equation of parabola