SOLUTION: Write the equation of the parabola with a focus (-2,4) and directrix y = 0.

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Write the equation of the parabola with a focus (-2,4) and directrix y = 0.       Log On


   

Question 876020: Write the equation of the parabola with a focus (-2,4) and directrix y = 0.
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi

Need to Know...............................................................

Standard Form of an Equation of a Circle is %28x-h%29%5E2+%2B+%28y-k%29%5E2+=+r%5E2 

Standard Form of an Equation of an Ellipse is %28x-h%29%5E2%2Fa%5E2+%2B+%28y-k%29%5E2%2Fb%5E2+=+1+ 

Standard Form of an Equation of an Hyperbola opening up and down is:%28y-k%29%5E2%2Fb%5E2+-+%28x-h%29%5E2%2Fa%5E2+=+1 

Standard Form of an Equation of an Hyperbola opening right and  left is:%28x-h%29%5E2%2Fa%5E2+-+%28y-k%29%5E2%2Fb%5E2+=+1 

the vertex form of a Parabola opening up(a>0) or down(a<0), y=a%28x-h%29%5E2+%2Bk

 the vertex form of a Parabola opening right(a>0) or left(a<0), x=a%28y-k%29%5E2+%2Bh



focus (-2,4) and directrix y = 0.

Parabola Opening Upward along x = -2: Directrix y = 0 below F(-2,4),

y=a%28x%2B2%29%5E2+%2Bk

((4-0)/2 = 2 = k

y=a%28x%2B2%29%5E2+%2B2 C(-2,2)

a = 1/(4p) = 1/(4*2) = 1/8

y=%281%2F8%29%28x%2B2%29%5E2+%2B2