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 

87. Find the equation of the normal at the point (am², am³) for the curve ay² = x³.

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

Find the equation of the tangent and normal to the curve