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Byju's Answer
Standard XI
Mathematics
Parametric Equation of a Circle
Write the par...
Question
Write the parametric equation of ellipse
(
x
−
3
)
2
25
+
(
y
+
2
)
2
16
=
1
.
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Solution
Given equation of ellipse is
(
x
−
3
)
2
25
+
(
y
+
2
)
2
16
=
1
let
X
=
x
−
3
,
Y
=
y
+
2
⟹
X
2
5
2
+
Y
2
4
2
=
1
This is in the form of the ellipse
x
2
a
2
+
y
2
b
2
=
1
⟹
a
=
5
,
b
=
4
The parametric equation of this ellipse is
x
=
a
cos
θ
,
y
=
b
sin
θ
⟹
X
=
5
cos
θ
,
Y
=
4
sin
θ
⟹
x
−
3
=
5
cos
θ
,
y
+
2
=
4
sin
θ
⟹
x
=
3
+
5
cos
θ
,
y
=
−
2
+
4
sin
θ
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