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Byju's Answer
Standard XII
Mathematics
Parametric Representation: Ellipse
If ( √(3) )bx...
Question
If
(
√
3
)
b
x
+
a
y
=
2
a
b
is tangent to the ellipse
x
2
a
2
+
y
2
b
2
=
1
, then eccentric angle
θ
is
A
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B
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C
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D
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Solution
The correct option is
B
Equation of tangent at a point
(
a
c
o
s
θ
,
b
s
i
n
θ
)
i
s
x
a
c
o
s
θ
+
y
b
s
i
n
θ
=
1
But, it is the same as
x
a
√
3
2
+
y
b
.
1
2
=
1
∴
c
o
s
θ
=
√
3
2
,
s
i
n
θ
=
1
2
⇒
θ
=
π
6
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Similar questions
Q.
If
(
√
3
)
b
x
+
a
y
=
2
a
b
is tangent to the ellipse
x
2
a
2
+
y
2
b
2
=
1
, then eccentric angle
θ
is
Q.
If
(
√
3
)
b
x
+
a
y
=
2
a
b
touches the ellipse
x
2
a
2
+
y
2
b
2
=
1
, then the eccentric angle of the point of contact is
Q.
If
b
x
+
√
3
a
y
=
2
a
b
touches the ellipse
x
2
a
2
+
y
2
b
2
=
1
, then the eccentric angle of the point of contact is
Q.
If
x
a
+
y
b
=
√
2
touches the ellipse
x
2
a
2
+
y
2
b
2
=
1
,
then its eccentric angle
θ
is equal to
Q.
If the line
x
a
+
y
b
=
√
2
touches the ellipse
x
2
a
2
+
y
2
b
2
=
1
, then the eccentric angle
θ
of point of contact is equal to
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