SOLUTION: plz help me to find out the points of intersection of parabolas y^2=4x and x^2=64y

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Question 824702: plz help me to find out the points of intersection of parabolas y^2=4x and x^2=64y
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
Substitution Method:
1. Solve one equation for one of the variables.
Solving the first equation for x (by dividing each side by 4:
y%5E2%2F4+=+x
2. Substitute for the solved-for variable in the other equation:
(y^2/4)^2 = 64y
3. Solve the one-variable equation:
y%5E4%2F16+=+64y
Multiply by 16 to eliminate the fraction:
y%5E4+=+1024y
Subtract 1024y (to get a zero on one side):
y%5E4+-+1024y=+0
Factor out the GCF of y:
y%28y%5E3+-+1024%29=+0
Zero Product Property:
y+=+0 or y%5E3-1024+=+0
Solving the second equation...
y+=+0 or y%5E3=1024
y+=+0 or
4. Use the solution(s) to the one-variable equation to find the solution(s) for the other variable:
For y = 0:
%280%29%5E2+=+4x
so x = 0, making (0, 0) a point of intersection.
For y+=+8root%283%2C+2%29
%288root%283%2C+2%29%29%5E2+=+4x
64root%283%2C+4%29+=+4x
16root%283%2C+4%29+=+x
making (16root%283%2C+4%29, 8root%283%2C+2%29) a second point of intersection. Here's a graph to illustrate:

(Don't mind the colors.)