The angle made by a double ordinate of length 8a at the vertex of the parabola y 2 = 4ax is :
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Let PQ be a double ordinate of length 8a. Then PR = RQ = 4a. Coordinates of P and Q are (OR,4a)and (OR, – 4a) respectively. Since, P lies on the parabola y 2 = 4ax, therefore,
(4a) 2 = 4a(OR) ⇒ OR = 4a
Thus, the ordinates of P and Q are (4a, 4a) and (4a, –4a) respectively.
Now, m 1 = slope of OP = 
= 1 and m 2 = slope of OQ = 
= –1
Clearly, m 1 m 2 = –1
Thus, PQ makes a right angle at the vertex of the parabola.
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