Question

The circles x^2+y^2-8x+6y+21=0,  x^2+y^2+4x-10y-115=0
are​

Answer 1

Step-by-step explanation:

From point (1) ]

i) S 1

:x 2 +y 2−8x+6y+21=0 C 1≡ and r 1=2 S 2

:x 2+y 2+4x−10y−115=0 C1

:(−2,5) and r 2=12

∴C 1 C 2 =10 and r 2−R 1 =10 C 1 C 2 =r 2−R 1

∴S 1 and S 2 touches each other internally.

So, i is false

[ From point (1) ]

ii) S 1

:x 2 +y 2−4x−6y−12=0

C 1 ≡(2,3) and r 1=5 S 2

:x 2 +y 2 +6x−2y+1=0

C 2 ≡(−3,1) and r 2 =3

∴C 1 C 2= 29 and r

1−r 2=8

1−r 2 =2⇒r 1 +r 2 >C 1 C 2

So, S 1 and S 2 intersects each other ii is true.

Answer 2

Answer:

From point (1) ]

i) S 1

:x 2 +y 2−8x+6y+21=0 C 1≡ and r 1=2 S 2

:x 2+y 2+4x−10y−115=0 C1

:(−2,5) and r 2=12

∴C 1 C 2 =10 and r 2−R 1 =10 C 1 C 2 =r 2−R 1

∴S 1 and S 2 touches each other internally.