What is the equation in standard form of the parabola with a focus at (14,5)...

arrebolyt

arrebolyt

Answered

2022-01-28

What is the equation in standard form of the parabola with a focus at (14,5) and a directrix of y=-15?

Answer & Explanation

Madelyn Townsend

Madelyn Townsend

Expert

2022-01-29Added 13 answers

Explanation:
Focus is at (14,5) and directrix is y=-15. Vertex is at midway
between focus and directrix. Therefore vertex is at
(14, 5152) or (14, -5). The vertex form of equation of
parabola is y=a(xh)2+k; (h.k); being vertex. Here
h=14 and k=-5 So the equation of parabola is
y=a(x14)25. Distance of vertex from directrix is
d=15-5=10, we know d=14|a||a|=14d or
|a|=1410=140. Here the directrix is below
the vertex , so parabola opens upward and a is positive.
a=140 Hence the equation of parabola is
y=140(x14)25
mihady54

mihady54

Expert

2022-01-30Added 13 answers

Explanation:
the standard form of a parabola in translated form is.
(xh)2=4p(yk)
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
opens upwards
coordinates of vertex =(14,5152)=(14,5)
and p=5-(-5)=10
(x14)2=40(y+5) equation of parabola

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