COMEDK · Maths · 13. Parabola

The tangents drawn at the extremities of a focal chord of the parabola \(y^{2}=16 x\)

A intersect on \(x=0\)
B intersect on the line \(x+4=0\)
C intersect at an angle of \(60^{\circ}\)
D intersect at an angle of \(45^{\circ}\)

Verified Solution

Answer & Solution

Correct Answer

(B) intersect on the line \(x+4=0\)

Step-by-step Solution

Detailed explanation

The tangent at the extremities of a focal chord of a parabola intersect at right angles on the directrix. Now, equation of parabola is \(y^{2}=16 x\). So, its directrix is \(x=-4\) or \(x+4\). So, tangent intersect on the line \(x+4=0\).

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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