What is the sum of the intercepts of the line whose perpendicular distance from origin is 4 units and the angle which the normal makes with positive direction of x-axis is 15°?

What is the acute angle between the lines represented by the equations \({\rm{y}} - \sqrt 3 {\rm{x}} - 5 = 0\) and \(\sqrt 3 {\rm{y}} - {\rm{x}} + 6 = 0\) ?

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 ?

A straight line passes through the point of intersection of x + 2y + 2 = 0 and 2x - 3y - 3 = 0. It cuts equal intercepts in the fourth quadrant. What is the sum of the absolute values of the intercepts?

What is the acute angle between the pair of straight lines \(\sqrt 2 {\rm{x}} + \sqrt 3 {\rm{y}} = 1\) and  \(\sqrt 3 {\rm{x}} + \sqrt 2 {\rm{y}} = 2?\)

If the point (a, a) lies between the lines |x + y| = 2, then which one of the following is correct?

The area of the figure formed by the lines ax + by + c = 0, ax – by + c = 0, ax + by – c = 0 and ax – by – c = 0 is

The three lines 4x + 4y = 1, 8x – 3y = 2, y = 0 are

The points (a, b), (0, 0), (-a, -b) and (ab, b ²) are

Let x + 2y + 4 = 0 and -4x + 2y - 3 = 0 be the equations of two straight lines. Then

If the slope of the line joining the points (k, 4) and (-3, -2) is \(\frac{1}{2}\), then the value of k is

If the equation

3x² + 7xy + 2y² + 5x + 5y + k = 0

represents a pair of straight lines, then the value of k is

If the sum of the slopes of the lines given by x² - 2cxy - 7y² = 0 is four time their products, then the value of c is