Mathematics : Application of Derivatives

Find the slope of the normal at the point (am³ , am² ) to the curve a x² = y³.

Find a point on the curve y = (x – 2)² at which the tangent is parallel to the chord joining the points (2, 0) and (4, 4).

Find the point at which the tangent to the curve  has its slope 

Find the equation of the normal to the curve y² = 4x at the point (1, 2).

Find the equation of tangent to the ellipse 

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  y² = 4ax at the point (at², 2at).