Mathematics : Application of Derivatives

Show that the normal at any point 0 to the curve
x = a cosө + a ө sinө. y = a sin ө – a ө cos ө
is at a constant distance from the origin.

Find the equation of the tangent and normal to the given curves at the points given:
y = x² at (0,0).

Find the equation of the tangent and normal to the given curves at the points given:
y² = 4ax at (0, 0).

Find the equation of the tangent and normal to the given curves at the points given:
y = x³ at (1, 1)

Find the equation of the tangent and normal to the given curves at the points given:
y = x² at (2, 8)

Find the equation of tangent and normal to the hyperbola 

Find the equation of the tangent and the normal to the curve 

Find the equation of the tangent and normal to the curve