Tardigrade
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Tardigrade
Question
Mathematics
A tangent to the circle x2+y2=4 intersects the hyperbola x2-2 y2=2 at P and Q. If locus of mid-point of P Q is (x2-2 y2)2=λ(x2+4 y2), then λ equals
Q. A tangent to the circle
x
2
+
y
2
=
4
intersects the hyperbola
x
2
−
2
y
2
=
2
at
P
and
Q
. If locus of mid-point of
PQ
is
(
x
2
−
2
y
2
)
2
=
λ
(
x
2
+
4
y
2
)
, then
λ
equals
662
120
Conic Sections
Report Error
A
4
B
2
C
2
1
D
4
1
Solution:
Equation of chord of hyperbola
2
x
2
−
1
y
2
=
1
, whose mid-point is
(
h
,
k
)
is
2
h
x
−
k
y
=
2
h
2
−
1
k
2
(using
T
=
S
1
)
As, it is tangent to the circle
x
2
+
y
2
=
4
, so
∣
∣
4
h
2
+
k
2
2
h
2
−
k
2
∣
∣
=
2
⇒
(
2
h
2
−
k
2
)
2
=
4
(
4
h
2
+
k
2
)
⇒
Locus of
(
h
,
k
)
is
(
x
2
−
2
y
2
)
2
=
4
(
x
2
+
4
y
2
)
∴
λ
=
4