Question

Show that the circles x² + y2 – 8x – 2y+8 = 0 and x² + y2 – 2x+6y+6= 0) touch each other
and find the point of contact.​

Answer 1

Answer:

x^2+y^2-8x-2y+8=(x-4)^2+(y-1)^-16-1+8=0

(x-4)^2+(y-1)^2=3^2

So coordinates of the centre of this circle are 4,1

and its radius=3

Similarly second circle can be written as

(x-1)^2+(y+3)^2=2^2

So coordinates of the centre of this circle are 1, -3 and its radius=2

Distance between two origins = sq root of {(4-1)2+(1+3)^2}=5

=3+2= sum of radii of two circles

Hence two circles touch each other