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Mathematics
Problem
The circle
x
2
+
y
2
=
25
x^{2}+y^{2}=25
x
2
+
y
2
=
25
meets the rectangular hyperbola
x
y
=
k
xy=k
x
y
=
k
in the first quadrant. For which positive value of
k
k
k
do the two curves have a common tangent at their point(s) of intersection? a)
10
10
10
b)
25
4
\dfrac{25}{4}
4
25
c)
25
2
\dfrac{25}{2}
2
25
d)
5
5
5
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