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Byju's Answer
Standard XII
Mathematics
Equation of Pair of Tangents: Hyperbola
Write the coo...
Question
Write the coordinates of the point on the curve y
2
= x where the tangent line makes an angle
π
4
with x-axis.
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Solution
Let the required point be (x
1
, y
1
).
The tangent makes an angle of 45
o
with the x-axis.
∴ Slope of the tangent = tan 45
o
= 1
Since
,
the
point
lies
on
the
curve
.
Hence
,
y
1
2
=
x
1
Now
,
y
2
=
x
⇒
2
y
d
y
d
x
=
1
⇒
d
y
d
x
=
1
2
y
Slope of the tangent =
d
y
d
x
x
1
,
y
1
=
1
2
y
1
Given:
1
2
y
1
=
1
⇒
2
y
1
=
1
⇒
y
1
=
1
2
Now
,
x
1
=
y
1
2
=
1
2
2
=
1
4
∴
x
1
,
y
1
=
1
4
,
1
2
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Equation of Pair of Tangents: Hyperbola
Standard XII Mathematics
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