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Mathematics
Problem
A line parallel to the straight line
2
x
−
y
=
0
2x - y = 0
2
x
−
y
=
0
is tangent to the hyperbola
x
2
4
−
y
2
2
=
1
\frac{x^2}{4} - \frac{y^2}{2} = 1
4
x
2
−
2
y
2
=
1
at the point
(
x
1
,
y
1
)
(x_1, y_1)
(
x
1
,
y
1
)
. Then,
x
1
2
+
5
y
1
2
x_1^2 + 5y_1^2
x
1
2
+
5
y
1
2
is equal to (a) 10 (b) 5 (c) 6 (d) 8
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