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^\circ?

Explanation

The equation of the line in normal form is x\cos 15^\circ + y\sin 15^\circ = 4. The x-intercept a = \frac{4}{\cos 15^\circ} and the y-intercept b = \frac{4}{\sin 15^\circ}. The sum is 4(\frac{1}{\cos 15^\circ} + \frac{1}{\sin 15^\circ}) = 4(\frac{\sin 15^\circ + \cos 15^\circ}{\sin 15^\circ \cos 15^\circ}). Using the values \sin 15^\circ + \cos 15^\circ = \frac{\sqrt{6}}{2} and \sin 15^\circ \cos 15^\circ = \frac{1}{4}, the sum evaluates to 4(\frac{\sqrt{6}/2}{1/4}) = 8\sqrt{6}.

Related questions on Analytical Geometry (2D)

• Consider the following statements in respect of the line passing through origin and inclining at an angle of 75^{\circ} with the positive ...
• 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...
• The centre of the circle passing through origin and making positive intercepts 4 and 6 on the coordinate axes, lies on the line
• The centre of an ellipse is at (0,0), major axis is on the y-axis. If the ellipse passes through (3,2) and (1,6), then what is its ecc...