The triangle formed by the tangent to the parabola $y^{2} = 4 x$ at the point whose abscissa lies in the interval $[a^{2}, 4 a^{2}]$ , the ordinate and the $x$ -axis has the greatest area equal to

Question

The triangle formed by the tangent to the parabola y 2 = 4 x at the point whose abscissa lies in the interval [ a 2 , 4 a 2 ] , the ordinate and the x -axis has the greatest area equal to

TestHub · Accepted Answer

P ≡ ( h 2 , 2 h ) tan θ = h 1 ​ And △ PTM = 2 1 ​ × 2 h × 2 h cot θ = 2 h 3 a 2 ≤ h 2 ≤ 4 a 2 ∴ maximum area = 2 ( 2 a ) 3 = 16 a 3

Mathematics - Parabola Question with Solution | TestHub

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