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From an external point P, two tangent lines are drawn to the parabola y² = 4x. If theta1 and theta2 are the angles these tangents make with the x-axis and theta1 + theta2 = pi/4, find the locus of P.
- x - y + 1 = 0
- x + y - 1 = 0
- x - y - 1 = 0
- x + y + 1 = 0
Correct answer: x - y - 1 = 0
Solution
Writing the tangency condition through P gives a quadratic in m whose roots' sum and product, combined with tan(pi/4) = 1, yield the linear locus x - y - 1 = 0.
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