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Mathematics
Mathematics
Problem
Let the normals at all the points on a given curve pass through a fixed point
(
a
,
b
)
(a, b)
(
a
,
b
)
. If the curve passes through
(
3
,
−
3
)
(3, -3)
(
3
,
−
3
)
and
(
4
,
−
2
2
)
(4, -2\sqrt{2})
(
4
,
−
2
2
)
, and given that
a
−
2
2
b
=
3
a-2\sqrt{2}b=3
a
−
2
2
b
=
3
then
(
a
2
+
b
2
+
a
b
)
(a^2+b^2+ab)
(
a
2
+
b
2
+
ab
)
is equal to
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