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From a point P, three normals are drawn to the parabola y² = 4x; two of them make angles with the x-axis whose tangents have product 2. The locus of P is part of a conic C. Identify the type of conic that is the locus of P.
- parabola
- circle
- ellipse
- hyperbola
Correct answer: parabola
Solution
The condition that the product of two slopes is constant (= 2) imposes a relation on (h,k) that turns out to be a parabola.
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