Question

p?= a. If p and pare the lengths of perpendicular drawn from the origin upon the lines X sec a + y coseca - a = 0 and x cosa. -- y sina. - a cos 2a, = 0, prove that 4p?

Answer 1

To prove that 4p= a, we need to find the lengths of the perpendiculars drawn from the origin to the given lines and show that they are equal.

Step-by-step explanation:

To prove that 4p= a, we need to find the lengths of the perpendiculars drawn from the origin to the given lines and show that they are equal.

Let's start with the first line: X sec a + y coseca - a = 0.

To find the length of the perpendicular, we need to determine the distance from the origin to the line. In this case, the perpendicular distance is equal to the coefficient of a in the equation, which is a. So, the length of the perpendicular for the first line is p.

Now, let's move on to the second line: x cosa. -- y sina. - a cos 2a = 0.

Similarly, the perpendicular distance from the origin to this line is equal to the coefficient of a in the equation, which is also a. So, the length of the perpendicular for the second line is also p.

Since the lengths of the perpendiculars for both lines are equal to p, we can conclude that 4p= a.