Question

A tangent at a point on the circle x2 + y2 = a.
intersect a concentric circle 'S' at P and Q. The
tangents of this circle at P, meet on the circle
x² + y2 = b2 then the equation of concentric
circle is​

Answer 1

Answer:

Step-by-step explanation:

Take, any point on x  

2

+y  

2

=b  

2

 as P(bcosθ,bsinθ)

From P (bcosθ,bsinθ) take

a chord of contact of circle S.

This chord of contact is tangent to x  

2

+y  

2

=a  

2

 

Chord of contact to circle S: x  

2

+y  

2

=r  

2

 

is

xx  

1

​  

+yy  

1

​  

−r  

2

=0

xbcosθ+ybsinθ−r  

2

=0

∴ distance of (0,0) to $$xbcos\theta+b

sin \theta y-r^{2}=0$$ is a.

∣  

b  

2

 

​  

 

r  

2

 

​  

∣=a

r  

2

=ab.

∴r=  

ab

​  

 

∴ equation of circle S is

x  

2

+y  

2

=r  

2

 

→x  

2

+y  

2

=ab