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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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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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