TS EAMCET · Maths · Parabola

If a normal chord of a parabola \(y^2=4 a x\) subtends a right angle at the origin, then the slope of that normal chord is

A \(\pm 2\)
B \(\pm 2 \sqrt{2}\)
C \(\pm \frac{1}{\sqrt{2}}\)
D \(\pm \sqrt{2}\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(\pm \sqrt{2}\)

Step-by-step Solution

Detailed explanation

Equation of the normal to parabola \(y^2=4 a x\) at \(\left(a t^2, 2 a t\right)\) \( y+t x=2 a t+a t^3 \) Suppose, it meets the parabola at \(Q\) and If \(O\) is the vertex of the parabola, then combine equation of \(O P\) and \(Q Q\) is a homogeneous equation of second degree.…

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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