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A point P moves such that its chord of contact with respect to the parabola y² = 12x coincides with a tangent line to the parabola y² = 4x. Find the locus of point P.
- y² = 36x
- y² = 9x
- y² = 18x
- y² = 6x
Correct answer: y² = 36x
Solution
The chord of contact ky = 6(x+h) gives slope m = 6/k and intercept 6h/k. For tangency to y² = 4x, the intercept must equal 1/m = k/6, giving 6h/k = k/6, so k² = 36h. The locus is y² = 36x.
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