Q. The length of the double ordinate of the parabola $ {{x}^{2}}=8y $ is $8$. Then, the end points of this double ordinate are
Rajasthan PETRajasthan PET 2004
Solution:
The length of double ordinate of parabola $ =8=PQ $
$ \therefore $ $ PR=RQ=4 $
$ \therefore $ Coordinates of P and Q will be
$ (-4,{{y}_{1}}) $ and $ (4,{{y}_{1}}) $ Since, P lies on $ {{x}^{2}}=8y $
$ \therefore $ $ {{(-4)}^{2}}=8{{y}_{1}}\Rightarrow 16=8{{y}_{1}}\Rightarrow {{y}_{1}}=2 $
Hence, coordinates of end points of double ordinate are (4, 2) and $ (-4,2) $ .
