Find all the tangents to the curve y = cos(x + y). -20 sxs 27 that are parallel to to the line x + 2y =
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Answer:
Equation of tangent is
dx
dy
=
2
3x−2
1
×3 at (h,k)slope of tangent=
2
3h−2
3
Given tangent is parallel to line 4x−2y+5 so slope of tangent=slope of line
⇒
2
3h−2
3
=2
⇒9=16(3h−2)
⇒3h=2+
16
9
⇒h=
48
41
∵(h
1
k) lies on curve so
k=
3h−2
=
3×
48
41
−2
=
16
9
=
4
3
∴(h
1
k)=(
48
41
,
4
3
)
eqn of tangent is y−
4
3
=2(x−
48
41
)
⇒4y−3=
48
8
(48x−41)
⇒24y−18=40x−41
⇒
$48x-24y=23$
eqn of normal is y−
4
3
=
2
−1
(x−
48
41
)
⇒4y−3=
48
−2
(48x−41)
⇒96y−72=−48x+41
⇒
$48x+96
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