SOLUTION: Determine the vertex, focus, directrix, and axis of symmetry of the parabola with the given equations: 1. X2 = -4y 2. 3y2 = 24x 3. (y + 5/2)2 = -5(x - 2/9)

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Determine the vertex, focus, directrix, and axis of symmetry of the parabola with the given equations: 1. X2 = -4y 2. 3y2 = 24x 3. (y + 5/2)2 = -5(x - 2/9)      Log On


   

Question 1091307: Determine the vertex, focus, directrix, and axis of symmetry of the parabola with the given equations:
1. X2 = -4y
2. 3y2 = 24x
3. (y + 5/2)2 = -5(x - 2/9)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

1.
%28x-h%29%5E2=+4p%28y-k%29 is the standard equation for an up-down facing parabola
you have
x%5E2=-4y or
%28x-0%29%5E2=+4p%28y-0%29+
vertex is at: (0,0)
4p=-4 =>+p=-1
focus: (0, -1)
directrix is above vertex p units: y+=+1
2.
3y%5E2+=+24x
y%5E2+=+8x+-> %28y-0%29%5E2=+4p%28x-0%29
4p=8->p=2
vertex is at: (0,0)
focus:(2, 0)
directrix:x+=+-2

3.
%28y+%2B+5%2F2%29%5E2+=+-5%28x+-+2%2F9%29 -> %28y-k%29%5E2=+4p%28x-h%29
->h=2%2F9, k=-5%2F2
4p=-5->p=-5%2F4
vertex: (2%2F9, -5%2F2)
focus: (2%2F9-5%2F4, -5%2F2)=(-37%2F36, -5%2F2)
directrix:+x+=2%2F9%2B5%2F4=+53%2F36