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The triangle PQR of area 'A' is inscribe...

The triangle PQR of area 'A' is inscribed in the parabola `y^2=4ax` such that the vertex P lies at the vertex pf the parabola and base QR is a focal chord.The modulus of the difference of the ordinates of the points Q and R is :

Text Solution

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slope of OQ=slope of OR
`Q(at_1^2,2at_1),R(at_2^2,2at^2)`
`A=[[0,0,1],[at^2,2at,1],[a/t^2,(-2a)/t,1]]`
`A=(at^2*(-2a)/t-2at*a/t^2)`
`A=|-2a^2t-(2a^2)/t|`
`A=2a^2(t+1/t)`
difference=`2a(t+1/t)`
`A/a=a(t+1/t)`
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