Find the points of intersection of the circles
x2 + y2 – 2 x + 2 y = 23 and x2 + y2 = 25.
Answers
Answer:
pata nahi
sorry I am very sorry
Answer:
radii then if the circles touch each other,
C
1
C
2
=R+r
Consider equation 1
(x+g)
2
+(y+f)
2
=g
2
+f
2
Similarly,
(x+g
1
)
2
+(y+f
1
)
2
=(g
1
)
2
+(f
1
)
2
Therefore
C
1
C
2
=R+r implies,
(g−g
1
)
2
+(f−f
1
)
2
=
g
2
+f
2
+
(g
1
)
2
+(f
1
)
2
Squaring both sides
(g−g
1
)
2
+(f−f
1
)
2
=g
2
+(g
1
)
2
+f
2
+(f
1
)
2
+2
g
2
+f
2
.
(g
1
)
2
+(f
1
)
2
g
2
+(g
1
)
2
+f
2
+(f
1
)
2
−2gg
1
−2ff
1
=g
2
+(g
1
)
2
+f
2
+(f
1
)
2
+2
g
2
+f
2
.
(g
1
)
2
+(f
1
)
2
−2gg
1
−2ff
1
=2
g
2
+f
2
.
(g
1
)
2
+(f
1
)
2
−gg
1
−ff
1
=
g
2
+f
2
.
(g
1
)
2
+(f
1
)
2
Squaring both sides, we get
(gg
1
)
2
+(ff
1
)
2
+2gg
1
ff
1
=(g
2
+f
2
).((g
1
)
2
+(f
1
)
2
)
(gg
1
)
2
+(ff
1
)
2
+2gg
1
ff
1
=(gg
1
)
2
+(ff
1
)
2
+(gf
1
)
2
+(fg
1
)
2
2gg
1
ff
1
=(gf
1
)
2
+(fg
1
)
2
(gf
1
)
2
+(fg
1
)
2
−2gg
1
ff
1
=0
(gf
1
−fg
1
)
2
=0
gf
1
=fg
1