1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard XII
Mathematics
Centroid
If Acosα, s...
Question
If
A
(
cos
α
,
sin
α
)
,
B
(
sin
α
,
−
cos
α
)
,
C
(
1
,
2
)
are the vertices of a
Δ
A
B
C
, then as a
α
varies, then find the locus of its centroid.
Open in App
Solution
Let
(
h
,
k
)
be the coordinates of the centroid of ∆ABC.
Thus
3
h
=
cos
a
+
sin
a
+
1
and
3
k
=
sin
a
−
cos
a
+
2
⇒
(
3
h
−
1
)
2
+
(
3
k
−
2
)
2
=
2
Hence locus of
(
h
,
k
)
is
(
3
x
−
1
)
2
+
(
3
y
−
2
)
2
=
2
9
x
2
+
9
y
2
−
6
x
−
12
y
+
3
=
0
3
x
2
+
3
y
2
−
2
x
−
4
y
+
1
=
0
Suggest Corrections
0
Similar questions
Q.
If
A
(
cos
α
,
sin
α
)
,
B
(
sin
α
,
−
cos
α
)
,
C
(
1
,
2
)
are the vertices of
Δ
A
B
C
, then as
α
varies, the locus of its centroid is
Q.
If
A
(
cos
α
,
sin
α
,
0
)
,
B
(
cos
β
,
sin
β
,
0
)
,
C
(
cos
γ
,
sin
γ
,
0
)
are vertices of
Δ
A
B
C
and let
cos
α
+
cos
β
+
cos
γ
=
3
a
,
sin
α
+
sin
β
+
sin
γ
=
3
b
, then correct matching of the following is:
List : I
List : II
A. Circumcentre
1.
(
3
a
,
3
b
,
0
)
B. Centroid
2.
(
0
,
0
,
0
)
C. Ortho centre
3.
(
a
,
b
,
0
)
Q.
If
A
(
cos
X
,
sin
X
)
,
B
(
sin
X
,
−
cos
X
)
,
C
(
−
2
,
1
)
are the vertices of a
△
A
B
C
,
then as
A
varies the locus of its centroid is:
Q.
Statement
I
:
A
(
0
,
0
),
B
(
cos
α
,
sin
α
)
,
C
(
−
sin
α
,
cos
α
)
are vertices of a triangle then the locus of the centroid of triangle is
9
x
2
+
9
y
2
=
4
Statement
I
I
: The locus of the point (
a
cos
θ
,
b
sin
θ
) is
x
2
a
2
+
y
2
b
2
=
1
Which of the above statement is/are correct:
Q.
The locus of the point of intersection of the lines
x
cos
α
+
y
sin
α
=
a
and
x
sin
α
−
y
cos
α
=
b
where
α
is variable is -
View More
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Related Videos
Basic Concepts
MATHEMATICS
Watch in App
Explore more
Centroid
Standard XII Mathematics
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
AI Tutor
Textbooks
Question Papers
Install app