Multiple choice general knowledge math & puzzles

If y = 2x + k is tangent to y^2 = 8x, then k =

  1. 3

  2. 2

  3. 1

  4. 1/2

Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For the line y = 2x + k to be tangent to the parabola y² = 8x, the system must have exactly one solution. Substituting x = (y - k)/2 into y² = 8x gives y² = 4(y - k), or y² - 4y + 4k = 0. For tangency, the discriminant must be zero: (-4)² - 4(1)(4k) = 0, so 16 - 16k = 0, giving k = 1.

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