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Byju's Answer
Standard XII
Mathematics
Length of Intercept Made by a Circle on a Straight Line
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Question
Solve this:
Q.9. Find the equation to the straight line which bisects, and is perpendicular to the straight line joining the points A (a, b) and B (a', b').
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Solution
Dear student
The
slope
of
the
line
joining
the
points
A
a
,
b
and
B
a
'
,
b
'
=
b
'
-
b
a
'
-
a
Hence
slope
of
the
line
⊥
to
it
will
be
=
-
a
'
-
a
b
'
-
b
The
mid
point
of
the
line
A
a
,
b
and
B
a
'
,
b
'
=
a
+
a
'
2
,
b
+
b
'
2
Hence
required
equation
is
given
by
:
y
-
b
+
b
'
2
=
-
a
'
-
a
b
'
-
b
x
-
a
+
a
'
2
⇒
2
y
-
b
-
b
'
2
=
a
-
a
'
b
'
-
b
2
x
-
a
-
a
'
2
⇒
2
y
-
b
-
b
'
=
a
-
a
'
b
'
-
b
2
x
-
a
-
a
'
⇒
b
'
-
b
2
y
-
b
-
b
'
=
a
-
a
'
2
x
-
a
-
a
'
⇒
2
yb
'
-
bb
'
-
b
'
2
-
2
yb
+
b
2
+
bb
'
=
2
ax
-
a
2
-
aa
'
-
2
xa
'
+
aa
'
+
a
'
2
⇒
2
(
a
-
a
'
)
x
+
2
(
b
-
b
'
)
y
=
a
2
+
b
2
-
a
'
2
-
b
'
2
Regards
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