The triangle PQR of area 'A' is inscribed in the parabola y 2 = 4ax such that the vertex P lies at the vertex of the parabola and the base QR is a focal chord. The modulus of the difference of the ordinates of the points Q and R is:
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Equation of QR is 2x – (t 1 + t 2 ) y + 2at 1 t 2 = 0
2x – 
– 2a = 0 ...(1)
⊥ r distance from (0, 0) to the line (1) is
= 
Area = 
× QR × ⊥ r distance from origin
= 
a 
× 
A = a 2 
Now the difference of ordinates
= 
= 
= 2a 
= 
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