What is the equation of the tangent line to the parabola y^2 = 8*x at the point (2, 4)?
Answer and explanation
Correct answer: D. x - y + 2 = 0
- Step 1: Differentiate implicitly: 2y y' = 8, so y' = 4 / y.
- Step 2: At point (2, 4), the slope is m = 4 / 4 = 1.
- Step 3: Equation of tangent: y - 4 = 1*(x - 2), so y = x + 2, or x - y + 2 = 0.
Answer
x - y + 2 = 0.
Why not the others: 2x - y = 0 uses slope 2 instead of 1; x + y - 6 = 0 uses slope -1; x - 2y + 6 = 0 uses slope 1/2.
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