Application of ...

If the tangent at $$(x_{1}, y_{1})$$ to the curve $$x^{3}+y^{3}=a^{3}$$ meets the curve again at $$(x_{2}, y_{2})$$ then

The ordinate of all points on the curve $$y=\dfrac{1}{2\sin^{2}x+3\cos^{2}x}$$  where the tangent is horizontal, is

The curve given by $$x + y = {e^{xy}}$$ has an tangents parallel to the y-axis at the point

The slope of normal to the curve y= log (logx) at x = e is 

Number of possible tangents to the curve $$y = \cos \left( {x + y} \right), - 3\pi  \leqslant x \leqslant 3\pi $$, that are parallel to the line $$x + 2y = 0$$, is

The normal to the curve, $${x}^{2}+2xy-{3y}^{2}=0,\ at\left (1,1\right)$$:

Number of tangents drawn from the point $$\left (-1/2,0\right)$$ to the curve $$y={e}^{x}$$. (Here { } denotes fractional part function ). 

If the tangent at P of the curve $$y^2=x^3$$ intersects the curve again at Q and the straight lines OP, OQ ma angles $$\alpha, \beta$$ with the x-axis where 'O' is the origin then $$\tan\alpha/\tan\beta$$ has the value equal to?

A curve C has the property that if the tangent drawn at any point 'P' on C meets the coordinate axes at A and B, and P is midpoint of AB. If the curve passes through the point $$(1, 1)$$ then the equation of the curve is?

Let $$f$$ be continuous and differentiable function such that $$f(x)$$ and $$f^{'}(x)$$ have opposite sign everywhere. Then