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A line y = x + 8 is a tangent to a parabola of the form y² = 4ax (axis along the x-axis, vertex at the origin), touching it at the point (8, 16). Find the equation of this parabola.
- y² = 32x
- y² = 16x
- y² = 8x
- y² = 64x
Correct answer: y² = 32x
Solution
The tangency condition c = a/m with m = 1 and c = 8 gives a = 8, so the parabola is y² = 32x, and the point of contact (a/m², 2a/m) = (8,16) confirms it.
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