TS EAMCET · Maths · Parabola

Let $A (1, 2), B (4, - 4), C (2, 2 \sqrt{2})$ be points on the parabola $y^{2} = 4 x .$ If $α$ and $β$ respectively represent the area of $Δ A B C$ and the area of the triangle formed by the tangents at $A, B, C$ to the above parabola, then $α β =$

A $6$
B $3 \sqrt{2}$
C $9$
D $6 \sqrt{2}$

Verified Solution

Answer & Solution

Correct Answer

(C) $9$

Step-by-step Solution

Detailed explanation

Given: A1,2, B4,-4, C2,22 be points on the parabola y2=4x·α and β, respectively represent the area of ΔABC and the area of the triangle formed by the tangents at A, B, C to the above parabola Area of △ABC=121214-412221=32 So…

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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Let A1,2, B4,-4, C2,22 be points on the parabola y2=4x. If α and β respectively represent the area of ΔABC and the area of the triangle formed by the tangents at A, B, C to the above parabola, then αβ=

Step-by-step Solution

Let $A (1, 2), B (4, - 4), C (2, 2 \sqrt{2})$ be points on the parabola $y^{2} = 4 x .$ If $α$ and $β$ respectively represent the area of $Δ A B C$ and the area of the triangle formed by the tangents at $A, B, C$ to the above parabola, then $α β =$