What is the equation in standard form of the parabola

Gideon Oliver

Gideon Oliver

Answered question

2022-02-03

What is the equation in standard form of the parabola with a focus at (2,-4) and a directrix of y= 6?

Answer & Explanation

mixtyggc

mixtyggc

Beginner2022-02-04Added 15 answers

Explanation:
The general form for the equation of a horizontal directrix is y=k-f
The focus of a parabola with a horizontal directrix is of the general form (h,k + f)
Therefore, we can write these 3 equations that will help us:
h=2
-4=k+f
6=k-f
solve the last two equation for k and f:
k=1
f=-5
The vertex form of the equation of this type of parabola is:
y=a(xh)2+k
Because we are not given the value of a, substitute 14f for a:
y=14f(xh)2+k
Substitute our known values into the above equation:
y=14(5)(x2)2+1
Expand the square:
y=120(x24x+4)+1
Distribute - 120:
y=120x2+15x15+1
Combine the constants:
y=120x2+15x+45

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