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Mathematics
Mathematics
Problem
Prove that the line
l
x
+
m
y
+
n
=
0
lx + my + n = 0
l
x
+
m
y
+
n
=
0
touches the circle
(
x
−
a
)
2
+
(
y
−
b
)
2
=
r
2
(x - a)^2 + (y - b)^2 = r^2
(
x
−
a
)
2
+
(
y
−
b
)
2
=
r
2
if
(
a
l
+
b
m
+
n
)
2
=
r
2
(
l
2
+
m
2
)
(al + bm + n)^2 = r^2(l^2 + m^2)
(
a
l
+
bm
+
n
)
2
=
r
2
(
l
2
+
m
2
)
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