question_answer

The length of the double ordinate of the parabola\[{{x}^{2}}=8y\]is 8. Then, the end points of this double ordinate are

A)  \[(4,2),(4,-2)\]      

B)  \[(2,4),(2,-4)\]

C)  \[(4,2),(-4,2)\]     

D) \[(-2,4),(2,4)\]

Correct Answer: C

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\[(-4,2)\].