Show that the end points of the latus rectum of the parabola x=2at, y=at^2 have parameters t=1 and t=-1.

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x=2at ,`y=at^2`

Thus equation f parabola

`x^2=4ay`

letus rectum passes trough focus and perpendcular to the axis of parabola.

when

y=a then `x^2=4a^2`

`x=+-2a`

Thus end point of latus rectum of the parabola x=2at ,`y=at^2`

`x=+-2a and y=a`  or when `t=+-1`

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