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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: |
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Answer» `pi/2` `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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