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Byju's Answer
Standard XII
Physics
Relating Circular Motion to SHM
The curve rep...
Question
The curve represented by
x
=
3
(
c
o
s
t
+
s
i
n
t
)
,
y
=
4
(
c
o
s
t
−
s
i
n
t
)
is
A
Ellipse
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B
Parabola
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C
Hyperbola
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D
Circle
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Solution
The correct option is
A
Ellipse
Given
x
3
=
cos
t
+
sin
t
&
y
4
=
cos
t
−
sin
t
Squaring these two,
⇒
x
2
9
=
1
+
2
sin
t
.
cos
t
.
.
.
(
i
)
y
2
16
=
1
−
2
sin
t
cos
t
.
.
.
.
(
i
i
)
Adding (i) & (ii)
x
2
9
+
y
2
16
=
2
⇒
x
2
18
+
y
2
32
=
1
So the equation represents ellipse.
Suggest Corrections
1
Similar questions
Q.
The curve with parametric equations
x
=
3
(
cos
t
+
sin
t
)
,
y
=
4
(
cos
t
−
sin
t
)
is
Q.
If
x
=
2
(
cos
t
−
sin
t
)
;
y
=
3
(
c
o
s
t
+
s
i
n
t
)
represents a conic, its foci are:
Q.
The curve represented by
x
=
3
cos
t
+
3
sin
t
and
y
=
4
cos
t
−
4
sin
t
is
Q.
If
x
=
3
(
cos
t
+
sin
t
)
;
y
=
2
(
cos
t
−
sin
t
)
represents a conic, then its foci are
Q.
If a curve is represented parametrically by
x
=
sin
(
t
+
7
π
12
)
+
sin
(
t
−
π
12
)
+
sin
(
t
+
3
π
12
)
,
y
=
cos
(
t
+
7
π
12
)
+
cos
(
t
−
π
12
)
+
cos
(
t
+
3
π
12
)
, then the value of
d
d
t
(
x
y
−
y
x
)
at
t
=
π
8
is
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