Consider the following statements in respect of the line passing through origin and inclining at an angle of 75° with the positive direction of x-axis :

1. The line passes through the point $\left(1, \frac{1}{2−\sqrt{3}}\right)$.

2. The line entirely lies in first and third quadrants.

Which of the statements given above is/are correct ?

If P(3, 4) is the mid-point of a line segment between the axes, then what is the equation of the line?

The base AB of an equilateral triangle ABC with side 8 cm lies along the y-axis such that the mid-point of AB is at the origin and B lies above the origin. What is the equation of line passing through (8, 0) and parallel to the side AC ?

Consider the inequations 5x - 4y + 12 < 0, x + y < 2, x < 0 and y > 0. Which one of the following points lies in the common region?