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Byju's Answer
Standard XII
Mathematics
Length of Intercept Made by a Circle on a Straight Line
Is 2x + 3y ...
Question
Is
2
x
+
3
y
=
0
a tangent from
(
−
3
,
2
)
to circle
x
2
+
y
2
+
10
x
+
2
y
+
13
? How to check like this if it is correct or not?
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Solution
x
2
+
y
2
+
10
x
+
2
y
+
13
=
(
x
+
5
)
2
+
(
y
+
1
)
2
−
13
=
0
Therefore, Center is
(
−
5
,
−
1
)
and radius is
√
13
The distance of the center from the line
2
x
+
3
y
=
0
is
|
2
(
−
5
)
+
3
(
−
1
)
|
√
2
2
+
3
2
is
√
13
.
Therefore, the line is the tangent to the circle.
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