The intercepts on x-axis made by tangents to the curve, 
, which are parallel to the line y = 2x, are equal to:
(1) 
(2) 
(3) 
(4) 
[JEE Main 2013]
Solution
If x > 0, 
Slope of tangent = 
Since the tangent is parallel to the line y = 2x whose slope = 2,
So, the point of contact is (2, 2) and the equation of the tangent is,
y – 2 = 2(x – 2)
Or, y = 2x – 2 whose intercept on the x-axis is 1.
If x < 0, 
Slope of tangent = 
Since the tangent is parallel to the line y = 2x whose slope = 2,
or x = -2
So, the point of contact is (-2, -2) and the equation of the tangent is,
y + 2 = 2(x + 2)
Or, y = 2x + 2 whose intercept on the x-axis is -1. Hence, option (1).