Tangents and it...

How many tangents are parallel to x-axis for the curve $$ y = x^2 - 4x + 3$$ ?

The slope of the tangent to the curve given by $$x = 1 - \cos { \theta  }$$, $$y = \theta -\sin { \theta  } $$ at $$\theta = \dfrac { \pi  }{ 2 } $$ is

The equations of tangent to the curve $$\left (\dfrac {x}{a}\right )^{n} + \left (\dfrac {y}{b}\right )^{n} = 2at, (a, b)$$ is $$5$$.

What is the slope of the tangent to the curve $$y=sin^{-1}(sin^2x)$$ at $$x=0$$ ?

Find the slope of the normal to the curve $$4x^3+6x^2-5xy-8y^2+9x+14=0$$T the point $$-2, 3$$.

A mirror in the first quadrant is in the shape of a hyperbola whose equation is xy = 1. A light source in the second quadrant emits a beam of light that hits the mirror at the point (2,1/2). If the reflected ray is parallel to the y-axis the slope of the incident beam is 

The equation to the tangent to the curve $$y={ be }^{ { -x }/{ a } }$$ at the point where it crosses the $$y$$-axis is

The point on the curve $$y = \sqrt {x - 1}$$ where the tangent is perpendicular to the line $$2x + y - 5 = 0$$ is

Consider the curve $$y = e^{2x}$$.Where does the tangent to the curve at (0, 1) meet the x-axis ? 

The equation to the normal to the hyperbola $$\dfrac {x^{2}}{16} - \dfrac {y^{2}}{9} = 1$$ at $$(-4, 0)$$ is.