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Byju's Answer
Standard XII
Mathematics
Equation of Circle with (h,k) as Center
The number of...
Question
The number of circle having radius 5 and passing through the points
(
−
2
,
0
)
and
(
4
,
0
)
is
A
One
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B
Two
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C
Four
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D
Infinite
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Solution
The correct option is
B
Two
let center of circle is
(
h
,
k
)
so
(
h
+
2
)
2
+
k
2
=
25
.......
(
1
)
and
(
h
−
4
)
2
+
k
2
=
25
.......
(
2
)
From equation
(
1
)
and
(
2
)
(
h
+
2
)
2
+
k
2
=
(
h
−
4
)
2
+
k
2
⇒
(
h
+
2
)
2
=
(
h
−
4
)
2
⇒
(
h
+
2
)
2
−
(
h
−
4
)
2
=
0
is of the form
a
2
−
b
2
⇒
(
h
+
2
+
h
−
4
)
(
h
+
2
−
h
+
4
)
=
0
where
a
2
−
b
2
=
(
a
+
b
)
(
a
−
b
)
⇒
6
(
2
h
−
2
)
=
0
or
h
=
1
Substituting
h
=
1
in eqn
(
1
)
we get
(
h
+
2
)
2
+
k
2
=
25
⇒
3
2
+
k
2
=
25
⇒
k
2
=
25
−
9
=
16
⇒
k
=
±
4
So two circles are possible.
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