JEE MAIN - Mathematics (2019 - 12th January Morning Slot - No. 9)
Let P(4, –4) and Q(9, 6) be two points on the parabola, y2 = 4x and let x be any point on the arc POQ of this parabola, where O is the vertex of this parabola, such that the area of $$\Delta $$PXQ is maximum. Then this maximum area (in sq. units) is :
$${{625} \over 4}$$
$${{125} \over 4}$$
$${{75} \over 2}$$
$${{125} \over 2}$$
Explanation
_12th_January_Morning_Slot_en_9_1.png)
y2 = 4x
2yy' = 4
y ' = $${1 \over t} = 2,$$ $$t = {1 \over 2}$$
Area = $${1 \over 2}\left| {\matrix{ {{1 \over 4}} & 1 & 1 \cr 9 & 6 & 1 \cr 4 & { - 4} & 1 \cr } } \right| = {{225} \over 4}$$
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