find the length of the chord intercepted by the circle x^2+y^2-x+3y-22=0 on the line y=×-3
answer please
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Answer:
Solution
To find the co-ordinates of the end of the chords, let us substitute the equation of the line in the circle.
Hence
x
2
+
(
x
−
3
)
2
−
x
+
3
(
x
−
3
)
−
22
=
0
⇒
x
2
+
x
2
−
6
x
+
9
−
x
+
3
x
−
9
−
22
=
0
⇒
2
x
2
−
4
x
−
22
=
0
⇒
x
2
−
2
x
−
11
=
0
⇒
x
=
2
±
√
4
+
44
2
Hence
x
=
1
±
2
√
3
Therefore
x
1
=
1
+
2
√
3
and
x
2
=
1
−
2
√
3
.
Hence
y
1
=
−
2
+
2
√
3
and
y
2
=
−
2
−
2
√
3
Hence the length of the chord is
D
=
√
(
x
2
−
x
1
)
2
+
(
y
2
−
y
1
)
2
=
√
(
4
√
3
)
2
+
(
4
√
3
)
2
=
√
96
=
4
√
6
units.
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