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Q.

If on a given base BC [B(0, 0) and C(2,0)], a triangle is described such that the sum of the tangents of the base angles is 4, then the equation of the locus of the opposite vertex A is a parabola whose directrix is, y = k. The value of k is

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answer is 2.125.

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Detailed Solution

Given tan⁡α⋅tan⁡β=4or  yx+y2−x=4or  y=2x(2−x)or  −y2=x2−2x=(x−1)2−1or  (x−1)2=−12(y−2)Directrix : y−2=18 or y=178
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If on a given base BC [B(0, 0) and C(2,0)], a triangle is described such that the sum of the tangents of the base angles is 4, then the equation of the locus of the opposite vertex A is a parabola whose directrix is, y = k. The value of k is