To find: The position of Q when P approaches to origin and the limiting position of Q.
The limiting position of Q is .
Slope of Perpendicular lines: The product of slope of the two perpendicular lines equal to –1.
The perpendicular bisector of OP intersects the y-axis as P approaches the origin along the parabola then the length of the Q will increases and joins at a point R on the parabola.
Let R be the midpoint of , since then .
Let and from figure 1that is .
The slope of is
By the slopes of the perpendicular lines
Let , bet the two points then the slope of is
From equations (1) and (2)
In above equation if x approaches 0,
Thus the required limiting position of Q is .
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