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Mathematics
Mathematics
Problem
The solution curves of the differential equation
(
x
d
x
+
y
d
y
)
x
2
+
y
2
=
(
x
d
y
−
y
d
x
)
(
1
−
x
2
−
y
2
)
(x dx + y dy) \sqrt{x^2 + y^2} = (x dy - y dx) \left( \sqrt{1 - x^2 - y^2} \right)
(
x
d
x
+
y
d
y
)
x
2
+
y
2
=
(
x
d
y
−
y
d
x
)
(
1
−
x
2
−
y
2
)
are circles of radius
a
b
\frac{a}{b}
b
a
, where
a
a
a
,
b
b
b
are natural number such that
HCF
(
a
,
b
)
=
1
\text{HCF}(a,b)=1
HCF
(
a
,
b
)
=
1
, then the value of
a
+
b
a+b
a
+
b
is
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