Calculate the radius of curvature at any point for the curve x= acos³t y= asin3t
Answers
Answered by
3
Answer:
Slope of normal to the curve = −
(
dx
dy
)
θ=π/4
1
x=acos
3
θ,y=asin
3
θ
dθ
dx
=3acos
2
θ(−sinθ),
dθ
dy
=3asin
2
θcosθ
∴
dx
dy
=
dx/dθ
dy/dθ
=
−3acos
2
θsinθ
+3asin
2
θcosθ
=−tanθ
∴(
dx
dy
)
θ=π/4
=−1
∴ Equation of normal =(y−y
0
)=
(
dx
dy
)
θ=π/4
−1
[x−x
0
]
y−
2
2
a
=
−1
−1
(x−
2
2
a
) [x
0
=acos
3
4
π
=
2
2
a
y−
2
2
a
=x−
2
2
a
y
0
=asin
3
4
π
=
2
2
a
]
y=x
Step-by-step explanation:
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Answered by
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Here's is your answer
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pritamraj2207:
i say x=acos³t y=asin3t
ok
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