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  • Let A ≡ (9, 6), B(4, -4) be two points on parabola <img alt="y^2=4 x \text { and } P\left(t^2, 2 t\right), t \in[-2,3]" src="https://entrancecorner.oncodecogs.com/g

Let A ≡ (9, 6), B(4, -4) be two points on parabola y^2=4 x \text { and } P\left(t^2, 2 t\right), t \in[-2,3] be a variable point on it such that area of ΔPAB is maximum, then point P will be 

 

Option: 1

 (4, 4)


Option: 2

(3,-2 \sqrt{3})


Option: 3

(4, 1)


Option: 4

\left(\frac{1}{4}, 1\right)


Answers (1)

best_answer

Let P be \left(\mathrm{t}^2, 2 \mathrm{t}\right) area of Δ PAB

\frac{1}{2}\left|\begin{array}{ccc} t^2 & 2 t & 1 \\ 9 & 6 & 1 \\ 4 & -4 & 1 \end{array}\right|=\left|5 t^2-5 t-30\right|

it is maximum at t = 1/2. 

 

Posted by

SANGALDEEP SINGH

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