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Solve this problem - Let A(4,-4) and B(9,6) be points on the parabola,. Let C be chosen on the arc AOB of the parabola, - Co-ordinate geometry - JEE Main

Let A(4,-4) and B(9,6) be points on the parabola, y^{2}=4x. Let C be chosen on the arc AOB of the parabola, where O is the origin,such that the area of \Delta ACB is maximum. Then, the area (in sq. units) of \Delta ACB is

  • Option 1)

     

    31\tfrac{3}{4}

  • Option 2)

     

    31\tfrac{1}{4}

  • Option 3)

     

    30\tfrac{1}{2}

  • Option 4)

     

    32

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A admin

 

Standard equation of parabola -

y^{2}=4ax

- wherein

Parabola

y^2 = 4x

Any point on the parabola is 

(at^2, 2at)

Here, a = 1

SO,

(t^2. 2t)

Aera = 5|t^2 -t -6|

        = 5\left|\left(t-\frac{1}{2} \right )^2 - \frac{25}{6}\right|

Aera is maximum when t=\frac{1}{2}

 


Option 1)

 

31\tfrac{3}{4}

Option 2)

 

31\tfrac{1}{4}

Option 3)

 

30\tfrac{1}{2}

Option 4)

 

32

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