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Byju's Answer
Standard XII
Mathematics
Direct Common Tangent
lx+my+n=0 is ...
Question
l
x
+
m
y
+
n
=
0
is a tangent line to the circle
x
2
+
y
2
=
r
2
if
A
l
2
+
m
2
=
n
2
r
2
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B
l
2
+
m
2
=
n
2
+
r
2
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C
n
2
=
r
2
(
l
2
+
m
2
)
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D
None of these
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Solution
The correct option is
C
n
2
=
r
2
(
l
2
+
m
2
)
line is tangent if
⇒
distance of line from center
=
r
∴
∣
∣
∣
l
(
0
)
+
m
(
0
)
+
n
√
l
2
+
m
2
∣
∣
∣
=
r
n
2
l
2
+
m
2
=
r
2
⇒
n
2
=
r
2
(
l
2
+
m
2
)
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0
Similar questions
Q.
The line
l
x
+
m
y
+
n
=
0
will be a tangent to the circle
x
2
+
y
2
=
a
2
iff