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Byju's Answer
Standard XII
Mathematics
Point Form of Tangent: Ellipse
The tangents ...
Question
The tangents are drawn to
x
2
28
+
y
2
16
=
1
making an angle
60
∘
with positive
x
−
axis, then the distance between tangents is
units
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Solution
For the given ellipse
x
2
28
+
y
2
16
=
1
a
2
=
28
,
b
2
=
16
Equation of tangent in slope form is
y
=
m
x
±
√
a
2
m
2
+
b
2
⋯
(
1
)
θ
=
60
∘
⇒
m
=
tan
θ
=
√
3
Putting values in equation
(
1
)
, we get
y
=
√
3
x
±
√
3
×
28
+
16
∴
y
=
√
3
x
±
10
Hence, the required distance is
d
=
|
10
+
10
|
√
1
+
3
=
10
units
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Point Form of Tangent: Ellipse
Standard XII Mathematics
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