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

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) (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:

2. Substitute for the solved-for variable in the other equation:
(y^2/4)^2 = 64y
3. Solve the one-variable equation:

Multiply by 16 to eliminate the fraction:

Subtract 1024y (to get a zero on one side):

Factor out the GCF of y:

Zero Product Property:
or
Solving the second equation...
or
or
4. Use the solution(s) to the one-variable equation to find the solution(s) for the other variable:
For y = 0:

so x = 0, making (0, 0) a point of intersection.
For

making (, ) a second point of intersection. Here's a graph to illustrate:

(Don't mind the colors.)
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