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PQ is double ordinateof a parabola y 2 =4ax. find the locus of its points of trisection.

PQ is double ordinateof a parabola y2 =4ax. find the locus of its points of trisection.

Grade:11

1 Answers

Arun
25757 Points
4 years ago
 
The equation y^2 = 4ax can be parametrised as: 
x = at^2, y = 2at. 

If the extremities of the double ordinate are (at^2, 2at) and (at^2, - 2at), then its points of trisection have ordinates y1 and y2 where: 
y1 = - 2at + 4at / 3 = 2at / 3 
y2 = - 2at + 8at / 3 = - 2at / 3 

For both of these points: 
y^2 = 4a^2 t^2 / 9 
y^2 = (4a / 9)(at^2) 
y^2 = 4(a / 9)x. 

The locus is the parabola y^2 = 4bx where: 
b = a / 9.
hence locus -
y^2 = (4/9) ax
 
hope it helps

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