Question

Find the envelope of the straight lines, down through the extremities of, and at right angles to the radii vectors of the following:
r = a + b cos@

Answer 1

Answer:

Let P is a Point where r = a(1+cosA) . B is Vertical Angle on It.

Than, Equation of Straight Line will be ( which is given in Question ) = rcos(A-B)= 2a[cos(B/2)]²

Now we have to Find Envelope of This :-

→ logr + logcos(A-B) = loga + logcos(B/2)

→ 0 + tan(A-B) = 0 - tan(B/2)

→ B= 2A - 2nπ

Putting This value in Equation now, we get,

→ rcos(2nπ-A)= 2a[cosA]²

→ r = 2acosA

Step-by-step explanation: