Find the centre of curvature and circle of curvature for the curve xy=c^2 at (c,c)

## Question

## Question

Find the centre of curvature and circle of curvature for the curve xy=c^2 at (c,c)

## Topic

Radius of curvature, Centre of curvature, Circle of curvature

## Radius of curvature

- Show that for the curve r (1-cos(theta)) =2a, the radius of curvature is (2/sqrt(a)). r^(3/2). (or) p^2 varies as r^3
- Find the radius of curvature of the curve r^n=a^n cos(n theta)
- Find the radius of curvature of the curve r^n=a^n sin(n theta)
- Find the radius of curvature for the curve r=a (1+cos(theta))
- Find the radius of curvature of the curve represented by x=a ((theta)+sin(theta)) and y=a (1-cos(theta))
- Find the radius of curvature at the point (3a/2, 3a/2) on the curve x^3+y^3=3axy
- Find the radius of curvature of the curve x^2+y^4=2 at the point (1, 1)
- For the curve y=ax/ (a+x), Show that (2ρ/a) ^ (2/3)=(x/y)^2+(y/x)^2
- Find the radius of curvature of the curve y=a log sec(x/a) at any point (x,y)
- Find the Radius of curvature for the curve y^2= (4a^2 (2a-x))/x where the curve meets the x-axis
- Find the radius of curvature of the cycloid x=a((theta)+sin(theta)), y=a (1-cos(theta))
- Find the Radius of curvature for the curve y^2= (a^2 (a-x))/x at the point (a,0)

## Centre of curvature, Circle of curvature

- Find the centre of curvature and circle of curvature for the curve y=x+9/x at (3,6)
- Find the centre of curvature and circle of curvature for the curve xy=c^2 at (c,c)
- Find the centre of curvature and circle of curvature for the curve y^2=12x at (x, y) = (3, 6)
- Find the centre of curvature and circle of curvature for the curve sqrt(x)+sqrt(y)=sqrt(a) at (a/4,a/4)