Tangents and it...

Find the points on the curve $$y=x^{3}$$, the tangents at which are inclined at an angle of $$60^{\circ}$$ to x-axis.

Find the points on the curve $$y=x/(1-x^{2})$$ where the tangents makes an angle of $$\pi /4$$ with x-axis

Find the equations of the tangents drawn to the curve $$\displaystyle y= x^{4}$$ which are drawn from the point (2,0).

If the normal to the curve $$y=f(x)$$ at the point $$(3,4) $$ makes an angle $$3\pi /4 $$ with the positive x-axis, then $$f'(3)=$$

The points of contact of the tangents drawn from the origin to the curve $$y=\sin{x}$$ lie on the curve

At what point p(x,y)of the curve $$\displaystyle y=e^{-\left | x \right |}$$ should a tangent  be drawn so that area of the triangle bounded by the tangent and the co-ordinate axes be greatest ?

If the tangent at the point $$\displaystyle \left ( at^{2},at^{3} \right )$$ on the curve $$\displaystyle ay^{2}= x^{3}$$ meets the curve again at Q.then the co-ordinates of Q is/are 

Find the co-ordinates of the points on the curve $$\displaystyle y= x/\left ( 1+x^{2} \right )$$ where the tangent to the curve has greatest slope.

The sum of the intercepts of a tangent to $$\displaystyle \sqrt{x}+\sqrt{y}=\sqrt{a}, a> 0$$ upon the coordinate axes is

The line $$y=x$$ is a tangent to the parabola $$\displaystyle y= ax^{2}+bx+c$$ at the point $$x=1$$.If the parabola passes through the point $$(-1,0)$$, then determine $$a, b, c.$$