Question

X2+ y2-2lx+g=0,X2+y2+2my-g=0

Answer 1

Step-by-step explanation:

Let the two circle be x

2

+y

2

+2gx+2fy+c=0

and x

2

+y

2

+2g

1

x+2f

1

y+c

1

=0

If the circles intersect at P then angle θ is

the angle between the tangents to both the circles at the point P.

C

1

and C

2

are centres of the circles.

⇒C

1

(−g,−f),C

2

(−g

1

,−f

1

) and

Radius are given by r

1

=

g

2

+f

2

−c

,r

2

=

g

1

2

+f

1

2

−c

1

d=∣C

1

C

2

∣=distance between the centres

⇒

g

2

+f

2

+g

1

2

+f

1

2

−2gg

1

−2ff

1

In △C

1

PC

2

cosα=

2r

1

r

2

r

1

2

+r

2

2

−d

2

where α is the ∠C

1

PC

2

θ is the angle A

′

PB

′

α+θ+90

∘

+90

∘

=360

∘

⇒α=180

∘

−θ

So, cos(180

∘

−α)=

2r

1

r

2

r

1

2

+r

2

2

−d

2