Find the distance between the points (cost + sin t, cost –sin t) and origin.
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Answer:
x=2cost+2tsint
dt
dx
=2tcost+2sint−2sint=2tcost
y=2sint−2tcost
dt
dy
=2cost+2tsint−2cost=2tsint
dx
dy
=
2tcost
2tsint
(t=
4
π
)
dx
dy
=1
dy
dx
=−1 for slope of normal.
x(
4
π
)=2cos(
4
π
)+2.
4
π
sin(
4
π
)=
2
(1+
4
π
)
y(
4
π
)=2sin(
4
π
)−2.
4
π
cos(
4
π
)=
2
(1−
4
π
)
Equation of normal with given point
x+y−2
2
=0
d=
2
(2
2)
=2
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