Question

Find the condition that the line 1/r= Acos@+Bsin@ may be a tangent to the conic 1/r=1+ecos@

Answer 1

Step-by-step explanation:

For the line,

x=rcosθ

y=rsinθ

So, it becomes

r

1

=

r

ax

+

r

by

⇒ax+by=1

For the circle

x=rcosθ

y=rsinθ

r=

r

2x

⇒x

2

+y

2

=2x

⇒(x−1)

2

+y

2

=1

Centre (1,0) and radius =1

For ax+by−1=0 to be tangent, perpendicular distance from (1,0) must be equal to 1

∣

∣

∣

∣

∣

∣

a

2

+b

2

a−1

∣

∣

∣

∣

∣

∣

=1

⇒(a−1)

2

=a

2

+b

2

⇒b

2

+2a=1