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JEE Main Math Class 11 Coordinate Geometry Part 3 Questions
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© examsnet.com
Question : 13
Total: 100
Let
P
and
Q
be two distinct points on a circle which has center at
C
(
2
,
3
)
and which passes through origin
O
. If
O
C
is perpendicular to both the line segments
C
P
and
C
Q
, then the set
{
P
,
Q
}
is equal to
[2021, 27 July Shift-1]
{
(
4
,
0
)
,
(
0
,
6
)
}
{
(
2
+
2
√
2
,
3
−
√
3
)
,
(
2
−
2
√
2
,
3
+
√
5
)
}
{
(
2
+
2
√
2
,
3
+
√
5
)
,
(
2
−
2
√
2
,
3
−
√
5
)
{
(
−
1
,
5
)
,
(
5
,
1
)
}
Validate
Solution:
Equation of circle is
(
x
−
2
)
2
+
(
y
−
3
)
2
=
(
2
−
0
)
2
+
(
3
−
0
)
2
⇒
(
x
−
2
)
2
+
(
y
−
3
)
2
=
13
Slope of
O
C
=
3
−
0
2
−
0
=
3
2
∴
Slope of
P
Q
=
−
2
3
=
tan
θ
Points at a distance of
√
13
units from 0
with slope
=
−
2
3
Using,
{
x
2
=
x
1
±
r
cos
θ
y
2
=
y
1
±
r
sin
θ
.
So,
x
2
=
2
±
√
13
(
3
√
13
)
=
2
±
3
∴
x
2
:
{
5
,
−
1
}
y
2
:
3
±
√
13
(
−
2
√
13
)
=
3
±
(
−
2
)
© examsnet.com
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