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Byju's Answer
Standard VIII
Mathematics
Equation of Circle Whose Extremities of a Diameter Given
If the points...
Question
If the points
(
2
,
0
)
,
(
0
,
1
)
,
(
4
,
5
)
and
(
0
,
c
)
are concyclic, then the value of
c
is ?
A
1
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B
13
3
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C
6
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D
8
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Solution
The correct options are
A
1
B
13
3
First find the equation of circle passes through point
(
2
,
0
)
,
(
0
,
1
)
and
(
4
,
5
)
Equation of the circle
x
2
+
y
2
+
2
g
x
+
2
f
y
+
c
=
0
so putting the points
4
+
4
g
+
c
=
0
.
.
.
.
.
.
.
.
.
.
.
.
.
[
1
]
1
+
2
f
+
c
=
0
.
.
.
.
.
.
.
.
.
.
.
.
.
.
[
2
]
39
+
8
g
+
10
f
+
c
=
0
.
.
.
.
.
.
.
.
.
.
.
.
[
3
]
solve these equation
g
=
−
25
12
f
=
−
8
3
c
=
13
3
so equation of circle
x
2
+
y
2
−
25
x
6
−
16
y
3
+
13
3
=
0
Now point
(
0
,
c
)
satisfy this equation
c
2
−
16
c
3
+
13
3
=
0
3
c
2
−
16
c
+
13
=
0
c
=
1
,
13
3
Suggest Corrections
0
Similar questions
Q.
If
(
2
,
0
)
,
(
0
,
1
)
,
(
4
,
5
)
and
(
0
,
C
)
are concyclics then find
C
Q.
The line
x
+
2
y
+
a
=
0
intersects the circle
x
2
+
y
2
−
4
=
0
at two distinct points
A
and
B
. Another line
12
x
−
6
y
−
41
=
0
intersects the circle
x
2
+
y
2
−
4
x
−
2
y
+
1
=
0
at two distinct points
C
and
D
. If the four points
A
,
B
,
C
, and
D
are concyclic then the value of
a
is
Q.
If A,B,C and D are concyclic points and
∠
B
A
C
=
45
o
. Find the value of
∠
B
D
C
Q.
If
(
2
,
0
)
,
(
0
,
1
)
,
(
4
,
5
)
and
(
0
,
c
)
are concyclic, then find
c
.
Q.
If the lines
a
1
x
+
b
1
y
+
c
1
=
0
and
a
2
x
+
b
2
y
+
c
2
=
0
cuts the coordinate axes in concyclic points, then
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