Circle $$C_{1}$$ has a radius of 3 units. The line segment PQ is the only diameter of the circle which is para

Question

Circle $$C_{1}$$ 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:

Accepted Answer

1 2 6 \frac{1}{\sqrt[6]{2}} 6 2 ​ 1 ​. Radius = 3 units, => Diameter = PQ = 6 units y-coordinates of P and Q are same as PQ is parallel to x-axis x-coordinates of P and Q will have a difference of 6 units. Equating y-coordinate of P and Q => a x = 2 a x + 6 a^x = 2 a^{x + 6} a x = 2 a x + 6 => 1 2 = a x + 6 a x \frac{1}{2} = \fr

Circle $C_{1}$ 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:

Circle $C_{1}$ 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:

Circle C1C_{1}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=axandy=2axy = a^{x} and y = 2a^{x}y=axandy=2ax respectively, where a < 1. The value of a is:

Circle C1C_{1}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=axandy=2axy = a^{x} and y = 2a^{x}y=axandy=2ax respectively, where a < 1. The value of a is:

Circle $C_{1}$ 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:

Circle $C_{1}$ 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: