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Question:

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 = a^x and y = 2a^x respectively, where a < 1. The value of a is:

Explanation:

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:

$y = a^{x} = 2 a^{(x + 6)}$

$a = {(1 / 2)}^{(\frac{1}{6})}$

Case 2:

$y = 2 a^{x} = a^{(x + 6)}$

$a = {(2)}^{(\frac{1}{6})}$

But it is given that a < 1

∴ Case 2 can be discarded

Hence, option (a).

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