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Mathematics
Mathematics
Problem
Locus of centroid of the triangle whose vertices are
(
a
cos
t
,
a
sin
t
)
,
(
b
sin
t
,
−
b
cos
t
)
(a \cos t, a \sin t), (b \sin t, -b \cos t)
(
a
cos
t
,
a
sin
t
)
,
(
b
sin
t
,
−
b
cos
t
)
and
(
1
,
0
)
(1, 0)
(
1
,
0
)
, where
t
t
t
is a parameter, is a.
(
3
x
−
y
)
2
+
(
3
y
)
2
=
a
2
−
b
2
(3x - y)^2 + (3y)^2 = a^2 - b^2
(
3
x
−
y
)
2
+
(
3
y
)
2
=
a
2
−
b
2
b.
(
3
x
−
y
)
2
+
(
3
y
)
2
=
a
2
+
b
2
(3x - y)^2 + (3y)^2 = a^2 + b^2
(
3
x
−
y
)
2
+
(
3
y
)
2
=
a
2
+
b
2
c.
(
3
x
+
y
)
2
+
(
3
y
)
2
=
a
2
+
b
2
(3x + y)^2 + (3y)^2 = a^2 + b^2
(
3
x
+
y
)
2
+
(
3
y
)
2
=
a
2
+
b
2
d.
(
3
x
+
y
)
2
+
3
y
2
=
a
2
−
b
2
(3x + y)^2 + 3y^2 = a^2 - b^2
(
3
x
+
y
)
2
+
3
y
2
=
a
2
−
b
2
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