SOLUTION: Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. Focus: (− 3/2, 0)

Algebra ->  Trigonometry-basics -> SOLUTION: Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. Focus: (− 3/2, 0)       Log On


   

Question 1176632: Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin.
Focus: (− 3/2, 0)

Found 2 solutions by MathLover1, ewatrrr:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
vertex at the origin-> h=0 and k=0
Focus: (-3%2F2, 0) -> parabola opens sideways to the left
so you need
y%5E2+=+4ax form
given -3%2F2
we get y%5E2+=+4+%28-3%2F2%29+x
y%5E2+=+2+%28-3%29+x
y%5E2+=+-6x



Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!

Hi
the vertex form of a Parabola opening right(a>0) or left(a<0), 
x=a%28y-k%29%5E2+%2Bh
where(h,k) is the vertex and y = k is the Line of Symmetry,
the focus is (h +p,k ), With Directrix x = (h - p) , a = 1/(4p)

V(0,0) F(-3/2,0)  Opens Left:  p = 1%2F%284a%29+=+-3%2F2  a = (-1/6)

x = (-1/6)y^2, the vertex form of a Parabola
Wish You the Best in your Studies.