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JEE Advanced 2020 Full Test 6 Paper 2
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© examsnet.com
Question : 38
Total: 54
Let
S
is the focus of parabola
y
2
=
4
a
x
and
X
is the foot of the directrix,
P
P
′
is a double ordinate of the curve and PX meets the curve again at Q. P'Q always passes through
(
A
)
(
a
,
0
)
(a, 0)
(
a
4
,
0
)
(
2
a
,
0
)
(
a
2
,
a
2
)
Validate
Solution:
Equation of
P
X
→
(
1
+
t
2
)
y
=
2
t
(
x
+
a
)
.
.
.
(
1
)
For point
Q
,
m
solving equation (1) & curve
t
2
(
x
+
a
)
2
=
a
x
(
1
+
t
2
)
2
(
x
−
a
t
2
)
(
x
t
2
−
a
)
=
0
x
=
a
t
2
⇒
∴
Q
=
(
a
t
2
,
2
a
t
)
Equation of
P
′
Q
⇒
(
x
−
a
)
+
(
t
2
−
1
2
t
)
(
y
)
=
0
Will always passes through
(
a
,
0
)
© examsnet.com
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