# find the radius of curvature at any point p(x,y) one the parabola y^2=4ax

## Answers

Answered by

0

**Given :** parabola y^2=4ax

**To Find : **radius of curvature at any point p(x,y)

**Solution:**

y² = 4ax

=> 2y dy/dx = 4a

=> dy/dx = 4a/2y

=> **dy/dx = 2a/y**

dy/dx = 2a/y

=> d²y/dx² = (-2a/y²) (dy/dx)

=> d²y/dx² = (-2a/y²)(2a/y)

=> **d²y/dx² = -4a²/y³**

R = radius of curvature

R = ( 1 + (dy/dx)²)^(3/2) / (d²y/dx²)

=> R = ( 1 + (2a/y)²)^(3/2) / (** **-4a²/y³)

=> R = ( y² + 4a²)^(3/2) / (** **-4a² )

=> **R = - ( y² + 4a²)^(3/2) / 4a²**

**Learn More:**

find the radius of curvature of the curve y2=x3+8at the point (-2,0 ..

https://brainly.in/question/4300854

Find radius of curvature of curve: x² + xy + y² = 4 at point (–2, 0 ...

https://brainly.in/question/18998082

Similar questions