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A curve C through the origin has the property that the normal at any point (x, y) on it passes through the fixed point (1, 0). Find the equation of a line that is tangent to both the curve C and the parabola y² = 4x.
- x = 0
- y = 0
- y = x + 1
- x + y + 1 = 0
Correct answer: y = 0
Solution
The normal-through-(1,0) condition yields (x-1)² + y² = 1, a circle through the origin centred at (1,0); the x-axis y = 0 is tangent to both this circle (at origin) and the parabola y² = 4x (at origin).
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