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CGP EDU Academic Team
Published on: August 14, 2026
Find the range of c for which the line y = mx + c touches the parabola y 2 = 8 (x + 2).
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
(– ∞ , – 4] ∪ [4, ∞ )
Sol. (mx + c) 2 = 8x + 16
m 2 x 2 + c 2 + 2mx c = 8x + 16
m 2 x 2 + 2mxc – 8x + c 2 – 16 = 0
m 2 x 2 + x(2mc – 8) + c 2 – 16 = 0
D = 0
(2mc – 8) 2 – 4m 2 (c 2 – 16) = 0
4m 2 c 2 + 64 – 32mc – 4m 2 c 2 + 64m 2 = 0
2m 2 – mc + 2 = 0
Now for m to be real
D ≥ 0
c 2 – 16 ≥ 0
c ∈ (– ∞ , –4] ∪ [4, ∞ )
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