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Byju's Answer
Standard XII
Mathematics
Number of Common Tangents to Two Circles in Different Conditions
The number of...
Question
The number of common tangents to the circle
x
2
+
y
2
=
4
and
x
2
+
y
2
−
6
x
−
8
y
−
24
=
0
is
A
0
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B
1
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C
3
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D
4
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Solution
The correct option is
D
1
Given circles are
x
2
+
y
2
=
4
...(1)
and
x
2
+
y
2
−
6
x
−
8
y
−
24
=
0
...(2)
Center of circle (1) is
C
1
≡
(
0
,
0
)
and radius
r
1
=
2
Center of circle (2) is
C
2
≡
(
3
,
4
)
and radius
r
2
Also
d
=
distance between the centers
=
C
1
C
2
=
5
Since
d
=
r
2
−
r
1
, therefore the given circles touch internally, as such they can have just
1
common tangent at the point of contact
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1
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Standard XII Mathematics
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