SOLUTION: Find the exact solution(s) of the system: x^2/4 - y^2 = 1 and x = y^2 + 1 a. (4, sqrt3), (4, -sqrt3), (-4, sqrt3), (-4, -sqrt3) b. (4, sqrt3), (-4, sqrt3), c. (2,1), (2, -1),

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find the exact solution(s) of the system: x^2/4 - y^2 = 1 and x = y^2 + 1 a. (4, sqrt3), (4, -sqrt3), (-4, sqrt3), (-4, -sqrt3) b. (4, sqrt3), (-4, sqrt3), c. (2,1), (2, -1),      Log On


   

Question 337121: Find the exact solution(s) of the system: x^2/4 - y^2 = 1 and x = y^2 + 1
a. (4, sqrt3), (4, -sqrt3), (-4, sqrt3), (-4, -sqrt3)
b. (4, sqrt3), (-4, sqrt3),
c. (2,1), (2, -1), (4, sqrt3), (4, -sqrt3)
d. (4, sqrt3), (4, -sqrt3)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1.x%5E2%2F4-y%5E2+=+1
2.x=y%5E2+%2B+1
From eq. 2,
y%5E2=x-1
Substitute into eq. 1,
x%5E2%2F4-%28x-1%29=1
x%5E2-4x%2B4=4
x%5E2-4x=0
x%28x-4%29=0
Two solutions:
x=0
Then from eq. 2,
y%5E2=-1
No solution
.
.
.
x-4=0
x=4
Then from eq. 2,
y%5E2=4-1
y%5E2=3
y=0+%2B-+sqrt%283%29
.
.
.
(4,-sqrt%283%29),(4,sqrt%283%29)