Tangents and it...

The equations of the tangents to the curve $$y = x^4$$ from the point (2, 0) not on the curve, are given by

For the curve $$ y=3\sin \theta\cos\theta,  x=e^{\theta}\sin \theta,  0\leq \theta\leq\pi$$; the tangent is parallel to $$x$$ -axis when $$\theta$$ is

The curve given by the equation $$y-e^{xy}+x=0$$ has a vertical tangent at the point

The sum of the intercepts made on the axes of coordinates by any tangent to the curve $$\sqrt{x}+\sqrt{y}=2$$ is equal to

If the circle $$x^{2}+y^{2}+2gx+2fy+c=0$$ is touched by $$y=x$$ at $$P$$ such that 
$$OP=6\sqrt{2},$$ then the value of $$c$$ is

The point on the curve  $$3y=6x-5x^3 $$, the normal at which passes through the origin is

The number of tangents to the curve $$x^{3/2} + y^{3/2}= 2a^{3/2}$$, $$a>0$$, which are equally inclined to the axes, is

If $$m$$ is the slope of a tangent to the curve $$e^y= 1+x^2$$, then 

If at each point of the curve $$y=x^3-ax^2 +x+1$$, the tangent is inclined at an acute angle with the positive direction of the $$x$$-axis, then

The distance between the origin and the tangent to the curve $$y = e^{2x} + x^{2}$$ drawn at the point $$x = 0$$ is