Slope of tangent and normal

FInd the slope of the tangent and normal to the curve y=(sin2x+cot x+2)^(2) at x=(pi)/(2)

The number of tangents and normals to the hyperbola (x^(2))/(16)-(y^(2))/(25)=1 of the slope 1 is

Find the slopes of the tangent and normal to the curve x^(3)+3xy+y^(3)=2 at (1, 1).

Equation of Tangent and normals and their lengths

Tangent and normal ex - 2

The distance between a tangent and a normal of same slope 2 ,of the parabola y^(2)=8x is equal to

Tangent || Normal

Find the slopes of the tangent and the normal to the curve y=sqrt(x) at x=9

Find the slopes of the tangent and the normal to the curve x y=6 at (1,\ 6)

Find the slopes of the tangent and the normal to the curve x=a(theta-sintheta) , y=a(1+costheta) at theta=-pi//2