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Byju's Answer
Standard XII
Mathematics
Intercept Form of a Line
If three poin...
Question
If three points
(
h
,
0
)
,
(
a
,
b
)
and
(
0
,
k
)
lie on a line, show that
a
h
+
b
k
=
1
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Solution
Since the lines
A
(
h
,
0
)
,
B
(
a
,
b
)
and
C
(
0
,
k
)
lie on the same line.
Slope of
A
B
=
Slope of
B
C
⇒
b
−
0
a
−
h
=
k
−
b
0
−
a
⇒
b
a
−
h
=
k
−
b
−
a
⇒
−
a
b
=
(
a
−
h
)
(
k
−
b
)
⇒
−
a
b
=
a
k
−
a
b
−
h
k
+
h
b
⇒
h
k
=
a
k
+
h
b
Divide both sides by
h
k
we get
h
k
h
k
=
a
k
h
k
+
h
b
h
k
or
a
h
+
b
k
=
1
Hence proved.
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If three point (
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