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Byju's Answer
Standard XII
Mathematics
Distance Formula
Find the equa...
Question
Find the equation to the circle passing through the points
(
0
,
a
)
and
(
b
,
h
)
, and having its centre on the axis of
x
.
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Solution
Let the centre of circle be (k,0), then the equation of circle become
x
2
+
y
2
−
2
k
x
+
c
=
0
.....
(
i
)
(
0
,
a
)
,
(
b
,
h
)
satisfies the equation as the circle passes through these points.
From equation
(
i
)
,
we get
a
2
+
0
+
c
=
0
⇒
c
=
−
a
2
Also, for
(
b
,
h
)
in
(
i
)
,
we get
b
2
+
h
2
−
2
k
b
−
a
2
=
0
⇒
k
=
b
2
+
h
2
−
a
2
2
b
Thus, the equation of circle is
x
2
+
y
2
−
b
2
+
h
2
−
a
2
b
x
−
a
2
=
0
i.e.
b
(
x
2
+
y
2
−
a
2
)
=
x
(
b
2
+
h
2
−
a
2
)
.
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