1.

PQ is a double ordinate of the parabolay^2 = 4ax . Tangents are drawn to parabola at P and Q, which meets the y axis at S, R respectively. If area of trapezium PQRS is equal to24a^2 , then angle subtended by RS at the focus of parabola is:

Answer»

`pi/2`
`tan^(-1)(3/4)`
`tan^(-1) ((-4)/(3))`
`pi/3`

Solution :`p(at_(1)^(2),2at_(1))""t_(2)=-t_(1)`
`Q(at_(2)^(2),2at_(2))`
Equation of tangent at P `""t_(1)y=x+at_(1)^(2)`
`S-=(0, at_(1))`
`R-=(0, -at_(1))`

Area of trapezium PQRS
`=(1)/(2)(2at_(1)+4at_(1))xxat_(1)^(2)=24a%^(2)`
`=3a^(2)t_(1)^(3)=24a^(2)`
`t_(1)^(3)=(24)/(3)=8`
`t_(1)=2`
`tan theta=(at_(1))/(a)=t_(1)=2`
Angle subtended by SR at focus
`tan 2 theta =(2 tan theta)/(1-tan^(2)theta)=(4)/(1-4)=(-4)/(3), alpha=tan^(-1)((-4)/(3))`


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