Tangents and it...

If the curves $$y^2 = 4ax$$ and $$xy = c^2$$ cut orthogonally then $$\dfrac{c^4}{a^4} =$$

The equation of the tangent to the curve $$y = b{e^{ -\dfrac{x}{a}}}$$ at a point , where $$x=0$$ is 

The equation of the normal to the curve $$y=x+\sin x \cos x$$ at $$x=\pi/2$$ is

The equation of the normal to the curve $$y=\sin x$$ at $$(0,0)$$ is

The equation of the curve passing through $$(1,3)$$ whose slope at any point $$(x,y)$$ on it is  $$\dfrac { y }{ { x }^{ 2 } }$$ is given by

An equation of the tangent to the curve $$y=x^{4}$$ from the point $$(2,0)$$ not on the curve is:

Find the points on the ellipse $$\dfrac{{{x^2}}}{4} + \dfrac{{{y^2}}}{9}=1$$ , on which the normals are parallel to the line $$3x-y=1$$.

Number of different points on the curve $$y^2=x(x+1)^2$$ where the tangent to the curve drawn at $$(1, 2)$$ meets the curve, is?

Find the slope of the normal to the curve $$2x^{2} - xy + 3y^{2} = 18$$ at $$(3,1)$$.

Area of the triangle formed by the tangent at $$x=2$$ on the curve $$y= \dfrac{8}{4+x^2}$$ with the coordinate axes is (in sq. units)