Question

Find the envelope of a straight line draw at right angles to end of the radii vectors of the cardiod
$r = a(1 + \cos \alpha )$
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Answer 1

||✪✪ QUESTION ✪✪||

Find the envelope of a straight line draw at right angles to end of the radii vectors of the cardiod r = a(1+cosA)

|| ✰✰ 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

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For One More Solution Refer to Image Now.

Answer 2

Step-by-step explanation:

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