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A triangle is constructed on a fixed base such that the sum of the tangents of the two base angles is constant. The locus of the apex (vertex opposite the base) is:
- a circle
- a parabola
- an ellipse
- a hyperbola
Correct answer: a parabola
Solution
Summing the two tangents gives an equation linear in y and quadratic in x, which is a parabola.
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