Tangents and it...

The equation of the tangent to the curve $$y = x + \dfrac{4}{{{x^2}}}$$ , that is parallel to the $$x-$$axis , is 

The coordinates of the feet of the normals drawn from the point (14, 7) to the curve $$y^2 - 16 x - 8y = 0$$ are

The slope of the tangent to the curve $$y=sinx$$ where it crosses the $$x-axis$$ is 

The equation of normal to the curve $$y=\left| { x }^{ 2 }-\left| x \right|  \right| $$ at $$x=-2$$ is

The equation of the normal at $$t=\dfrac{\pi}{2}$$ to the curve $$x=2\sin t, y=2\cos t$$ is?

The equation of the tangents at $$(2, 3)$$ on the curve $$y^{2}=ax^{3}+b$$ is $$y=4x-5$$ find the value of $$a$$ & $$b$$.

The equation of the tangent to the curve $$y=2\sin{x}+\sin{2x}$$ at $$x=\cfrac{\pi}{3}$$ on it is

Tangent drawn to $$y=ax^2+bx+c$$ at$$(5,4)$$ is parallel to $$x-axis.$$ If $$a$$ $$\epsilon $$ $$[2,4]$$. Then maximum value of c.

The Point (s) on the cure $${ y }^{ 3 }+{ 3x }^{ 2 }=12y$$ where the tangent is vertical (parallel to y-axis), is/are.

The angle made by the tangent line at (1, 3) on the curve $$y=4x-{ x }^{ 2 }$$ with $$\overset { - }{ OX } $$ is