find the radius of curvature of the curve ✓x+✓y=✓a at the point where the line y=x cuts it.
Answers
Answered by
1
Answer:
We have,
x
+
y
=
a
Differentiation this equation with respect to x and we get,
dx
d
(
x
+
y
)=
dx
d
a
2
x
1
+
2
y
1
dx
dy
=0
2
y
1
dx
dy
=−
2
x
1
dx
dy
=−
x
y
At point (x
1
,y
1
)
(
dx
dy
)
(x
1
,y
1
)
=−
x
1
y
1
We know that,
Equation of tangent.
y−y
1
=
dx
dy
(x−x
1
)
At point (x
1
,y
1
)
y−y
1
=−
x
1
y
1
(x−x
1
)
y
x
1
−y
1
x
1
=−
y
1
(x−x
1
)
y
x
1
−y
1
x
1
=−x
y
1
+x
1
y
1
y
x
1
+x
y
1
=y
1
x
1
+x
1
y
1
On divide
x
1
y
1
both side and we get,
x
1
y
1
y
x
1
+x
y
1
=
x
1
y
1
y
1
x
1
+x
1
y
1
y
1
y
+
x
1
x
=
y
1
+
x
1
x
1
x
+
y
1
y
=
a
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