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Byju's Answer
Standard X
Mathematics
Distance between Two Points on the Same Coordinate Axes
A ≡ t2,2t, B ...
Question
A
≡
(
t
2
,
2
t
)
,
B
≡
(
1
t
2
,
−
2
t
)
a
n
d
s
≡
(
1
,
0
)
,
t
h
e
n
1
S
A
+
1
S
B
i
s
e
q
u
a
l
t
o
A
2
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B
1
2
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C
1
5
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D
1
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Solution
The correct option is
D
1
A
=
(
t
2
,
2
t
)
B
=
(
1
t
2
,
−
2
t
)
S
=
(
1
,
0
)
Distance formula
=
√
(
x
2
−
x
1
)
2
+
(
y
2
−
y
1
)
2
S
A
=
√
(
t
2
−
1
)
2
+
(
2
t
−
0
)
2
=
√
t
4
+
1
−
2
t
2
+
4
t
2
=
√
t
4
+
1
+
2
t
2
=
√
(
t
2
+
1
)
2
S
A
=
t
2
+
1
S
B
=
√
(
1
t
2
−
1
)
2
+
(
−
2
t
−
0
)
2
=
√
1
t
4
+
1
−
2
t
2
+
4
t
2
=
√
1
t
4
+
1
+
2
t
2
=
√
(
1
t
2
+
1
)
2
=
1
t
2
+
1
S
B
=
1
+
t
2
t
2
Now
1
S
A
+
1
S
B
=
1
t
2
+
1
+
t
2
1
+
t
2
=
1
+
t
2
1
+
t
2
=
1
.
Suggest Corrections
5
Similar questions
Q.
If A (a
2
,2a) ,B
(1/a
2
,-2/a) and S( 1 ,0 ), then prove that 1/SA +1/SB =1
Q.
If
A
(
a
2
,
2
a
)
B
(
1
a
2
,
−
2
a
)
and S(1,0) then prove that
1
S
A
+
1
S
B
=
1
Q.
If
S
A
=
2
m
+
(
2
m
+
1
)
+
(
2
m
+
2
)
+
.
.
.
+
4
m
and
S
B
=
(
2
m
+
1
)
+
(
2
m
+
3
)
+
(
2
m
+
5
)
+
.
.
.
+
(
4
m
−
1
)
,
then
Q.
If
A
=
(
a
t
2
,
2
a
t
)
,
B
=
(
a
t
2
,
−
2
a
t
)
,
S
(
a
,
0
)
then
1
S
A
+
1
S
B
=
Q.
If
tan
a
,
tan
b
,
tan
c
,
tan
d
are the roots of the eqn
tan
(
45
°
+
θ
)
=
3
tan
3
θ
, then
1
tan
a
+
1
tan
b
+
1
tan
c
+
1
tan
d
is
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