The triangle `P Q R` of area `A` is inscribed in the parabola `y^2=4a x` such that the vertex `P` lies at the vertex of the parabola and the base `Q R` is a focal chord. The modulus of the difference of the ordinates of the points `Qa n dR` is `A/(2a)` (b) `A/a` (c) `(2A)/a` (d) `(4A)/a`

Options

A. A/2a
B. A/a
C. 2A/a
D. 4A/a

Answer

C

Explanation

(3) Difference of the ordinate
`d=|2at+(2a)/(t)|=2a|t+(1)/(t)|`

Now, area `(A)=(1)/(2)|(at^(2),2at,1),(a//t^(2),-2a//t,1),(0,0,1)|=a^(2)(t+(1)/(t))`
`or2a(t+(1)/(t))=(2A)/(a)`