Answer:
k ≥ 0
Step-by-step explanation:
To find the intersection between y = kx-2 and y² = 4x-x².
Substitute y = kx-2 into y² = 4x-x² like this:
(kx-2)² = 4x -x²
k²x² - 4kx + 4 = 4x - x²
k²x² + x² - 4kx -4x + 4 = 0
(k² + 1)x² + (-4k -4)x + 4 = 0
- Discriminant b^2 - 4ac comparing ax² + bx + c
(-4k -4)² - 4(k² + 1)(4) = 0
16k² + 32k + 16 - 16k² -16 = 0
32k = 0
k = 0/32 = 0
For there to be intersection, k ≥ 0.
