Question

If p, q are perpendicular distance from origin to the lines xcosα + ysinα = acos2α and xsecα + ycosecα = 2b then p2 + q2 = ______​

Answer 1

Answer:

The perpendicular distance from origin to the line ax+by+c=0 is given by

a

2

+b

2

∣c∣

.

Distance from origin to line xsecα+y cosecα=a is p.

So, p=

∣

∣

∣

∣

∣

sec

2

α+ cosec

2

α

a

∣

∣

∣

∣

∣

=

∣

∣

∣

∣

∣

2

2acosαsinα

∣

∣

∣

∣

∣

=

∣

∣

∣

∣

2

a

sin2α

∣

∣

∣

∣

→(1)

& similarly, q=

∣

∣

∣

∣

∣

∣

cos

2

α+sin

2

α

acos2α

∣

∣

∣

∣

∣

∣

=∣acos2α∣→(2)

Square and add (1) & (2), we get

⇒(2p)

2

+q

2

=a

2

⇒4p

2

+q

2

=a

2

Step-by-step explanation:

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