Let PQ be a focal chord of y² = 4ax (a 0). The tangents at P and Q intersect at a point lying on the line y = 2x + a. If chord PQ subtends an angle theta at the vertex of the parabola, find tan(theta).

Question

Let PQ be a focal chord of y² = 4ax (a > 0). The tangents at P and Q intersect at a point lying on the line y = 2x + a. If chord PQ subtends an angle theta at the vertex of the parabola, find tan(theta).

Accepted Answer

-2*sqrt(7)/3. The intersection of tangents lies on the directrix and on y = 2x + a, fixing t1+t2; using t1 t2 = -1 and the vertex-angle formula gives tan theta = -2 sqrt7/3 (this is the standard JEE 2013 answer).

Let PQ be a focal chord of y² = 4ax (a > 0). The tangents at P and Q intersect at a point lying on the line y = 2x + a. If chord PQ subtends an angle theta at the vertex of the parabola, find tan(theta).

Solution

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