Question

find the radius of curvature of the curve ✓x+✓y=✓a at the point where the line y=x cuts it.​

Answer 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

Answer 2

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