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XAT 2014 — QA & DI Question 13

Simple EquationsEasy

Circle C1 has a radius of 3 units. The line segment PQ is the only diameter of the circle which is parallel to the X axis. P and Q are points on curves given by the equations y = ax and y = 2ax respectively, where a < 1. The value of a is:

Answer & solution

  • 126    

  • B

    136    

  • C

    163​​​​​​​

  • D

    1 6

  • E

    None of the above

Solution

Points P and Q have the same Y coordinate but their X coordinates differ by 6 units (Since the diameter = 6 units)

We have two possible cases:

Case 1:

y=ax=2a(x+6)

a=(1/2)(16)

Case 2:

y=2ax=a(x+6)

a=(2)(16)

But it is given that a < 1

∴ Case 2 can be discarded

Hence, option (a).

XAT 2014 QA & DI Q13: Circle C 1 has a radius of 3 units. The line segment PQ is the only diameter of the circle which is parallel t — Solution | TheCATExam