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Byju's Answer
Standard XII
Mathematics
Cosine Rule
If P(at^2,2at...
Question
If P(at^2,2at),Q(a/t^2,-2a/t)andS(a,0)be any three points,show that1/SP+1/SQ is independent of t?
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Q.
If
P
and
Q
are two points whose coordinates are
(
a
t
2
,
2
a
t
)
and
(
a
t
2
,
−
2
a
t
)
respectively and
S
is the point
(
a
,
0
)
. Show that
1
S
P
+
1
S
Q
is independent of
t
.
Q.
Let
P
(
a
t
2
,
2
a
t
)
,
Q
,
R
(
a
r
2
,
2
a
r
)
be three points on a parabola
y
2
=
4
a
x
.
If
P
Q
is the focal chord and
P
K
,
Q
R
are parallel where the co-ordinates of
K
is
(
2
a
,
0
)
,
then the value of
r
is
Q.
P, Q are two points whose coordinates are
(
a
t
2
,
2
a
t
)
and
(
a
t
2
,
−
2
a
t
)
and S is a point whose coordinates is
(
a
,
0
)
, then
1
S
P
+
1
S
Q
is constant for all values of
t
.
Q.
Let
a
,
r
,
s
,
t
be nonzero real numbers. Let
P
(
a
t
2
,
2
a
t
)
,
Q
,
R
(
a
r
2
,
2
a
r
)
and
S
(
a
s
2
,
2
a
s
)
be distinct points on the parabola
y
2
=
4
a
x
. Suppose that
P
Q
is the focal chord and lines
Q
R
and
P
K
are parallel, where
K
is the point
(
2
a
,
0
)
.
The value of
r
is
Q.
Let
a
,
r
,
s
and
t
be non –zero real numbers. Let
P
(
a
t
2
,
2
a
t
)
,
Q
,
R
(
a
r
2
,
2
a
r
)
and
S
(
a
s
2
,
2
a
s
)
be distinct points on the parabola
y
2
=
4
a
x
. Suppose that
P
Q
is the focal chord and lines
Q
R
and
P
K
are parallel, where
K
is point
(
2
a
,
0
)
.
The value of
r
is
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