JEE MainMathematicsParabolaNumerical+4 / −1
Let PQ be a focal chord of length 6.25 units of the parabola y2 = 4x. If O is the vertex of the parabola, then 10 times the area (in sq. units) of POQ is equal to .
Numerical answer
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Correct answer: 25
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Parabola and its focus
Given parabola: Comparing with the standard form , we get So the focus is and the vertex is .
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Parametric points of a focal chord
A general point on the parabola is For , this becomes
If is a focal chord, then the corresponding parameters are and .
Hence,
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Use the length of focal chord
Length of focal chord of parabola with endpoints corresponding to and is
Here and , so
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Area of triangle
Since , area of is
Substituting
we get
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Compute the area
From step 3, Therefore,
So the area is
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Find 10 times the area
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Final answer
The derived answer matches the stored correct answer.
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