Question

please solve this sum ​

Answer 1

Answer:

Length of perpendicular from origin,

=

a

2

+b

2

−c

xsecα+ycscα=a

cosα

x

+

sinα

y

=a

⇒xsinα+ycosα−acosαsinα=0

p=−

sin

2

α+cos

2

α

−acosαsinα

=acosαsinα

xcosα+ysinα=acos2α⇒q=acos2α

∴p=acosαsinα,q=acos2α

∴4p

2

+q

2

=4(acosαsinα)

2

+(acos2α)

2

=4a

2

cos

2

αsin

2

α+a

2

cos

2

2α

=4a

2

cos

2

αsin

2

α+a

2

−4a

2

sin

2

αcos

2

α

=a

2

∴4p

2

+q

2

=a

2