Question

Calculate the centre of curvature of the curve y = x2
at (1, 0)

Answer 1

Answer:

The given equation of curve is,

y=x 2

Thus, slope of tangent to the curve is given by,

m=

dx

dy

∴m= dxd(x 2 )

∴m=2x

Slope of tangent at point (1,1) is,

m=2×1

∴m=2

Thus, equation of tangent at point (1,1) is given by two point form as,

y−y

1

=m(x−x

1

)

y−1=2(x−1)

∴y−1=2x−2

∴2x−y−1=0

∴y=2x−1