Answer:
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Given is the system of equations.
Solve it by substitution, y = 8x²:
- x² - y² = 1
- x² - (8x²)² = 1
- x² - 64x⁴ = 1
- 64x⁴ - x² + 1 = 0
Find the discriminant of the quadratic equation, if it is positive there are two real solutions, if zero then one solution, if negative then no solution.
- D = (-1)² - 4*64*1
- D = -255
Since D < 0 there are no real solutions (intersections).