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MHT CET 2019 Math Solved Paper
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© examsnet.com
Question : 1
Total: 50
If
P
(
x
1
,
y
1
)
is a point on the hyperbola
x
2
−
y
2
=
a
2
, then SP.S'P = .........
x
1
2
−
y
1
2
a
2
x
1
2
+
y
1
2
a
2
x
1
2
−
y
1
2
x
1
2
+
y
1
2
Validate
Solution:
∴
P
(
x
1
,
y
1
)
lie on
x
2
−
y
2
=
a
2
then;
x
1
2
−
y
1
2
=
a
2
⇒
x
1
2
−
a
2
=
y
1
2
.......(i)
∴
x
2
−
y
2
=
a
2
is an equation of rectangular hyperbola .
∴
e
=
√
2
S
P
=
e
x
1
−
a
=
√
2
x
1
−
a
S
′
P
=
e
x
1
+
a
=
√
2
x
1
−
a
∴
S
P
.
S
′
P
=
e
2
x
1
2
−
a
2
=
2
x
1
2
−
a
2
=
x
1
2
+
x
1
2
−
a
2
=
x
1
2
+
y
1
2
(from (i))
© examsnet.com
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