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Byju's Answer
Standard XII
Mathematics
Chord of Contact
T P and T Q a...
Question
T
P
and
T
Q
are tangents to the parabola
y
2
=
4
a
x
at
P
and
Q
.
If the chord
P
Q
passes through the fixed point
(
−
a
,
b
)
,
then the locus of
T
is
A
a
y
=
2
b
(
x
−
b
)
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B
b
x
=
2
a
(
y
−
a
)
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C
b
y
=
2
a
(
x
−
a
)
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D
a
x
=
2
b
(
y
−
b
)
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Solution
The correct option is
C
b
y
=
2
a
(
x
−
a
)
Let
T
≡
(
h
,
k
)
.
Chord of contact of
(
h
,
k
)
is given by
k
y
=
4
a
(
x
+
h
)
2
⇒
k
y
=
2
a
(
x
+
h
)
As it passes through
(
−
a
,
b
)
,
b
k
=
2
a
(
−
a
+
h
)
Hence, required locus is
b
y
=
2
a
(
x
−
a
)
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8
Similar questions
Q.
T
P
&
T
Q
are tangents to the parabola,
y
2
=
4
a
x
at
P
&
Q
.
If the chord
P
Q
passes through the fixed point
(
−
a
,
b
)
then the locus of
T
is
Q.
T
P
and
T
Q
are tangents to the parabola
y
2
=
4
a
x
at
P
and
Q
.
If the chord
P
Q
passes through the fixed point
(
−
a
,
b
)
,
then the locus of
T
is
Q.
Let
y
2
−
4
a
x
be a parabola and PQ be a focal chord of parabola. Let T be the point of intersection of tangents at P and Q. Then.
Q.
If
P
and
Q
are the points of contact of tangents drawn from the point
T
to
y
2
=
4
a
x
and
P
Q
be a normal of the parabola at
P
, then the locus of the point which bisects
T
P
is
Q.
Tangents are drawn from the points on a tangent of the hyperbola
x
2
−
y
2
=
a
2
to the parabola
y
2
=
4
a
x
. If all the chords of contact pass through a fixed point
Q
, then the locus of the point
Q
for different tangents on the hyperbola is
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