Tangents and it...

The equation of the tangent to the curve $$y=e^{-|x|}$$ at the point where the curve cuts the line $$x=1$$ is

The equation of the normal at $$x$$ $$=$$ $$2a$$ for the curve $$\displaystyle y=\frac{8a^{3}}{4a^{2}+x^{2}}$$ is

Equation of the tangent line to $$y=be^{\frac{-x}{a}}$$ where it crosses y-axis is

The portion of the tangent to xy $$=a^{2}$$ at any point on it between the axes is

Area of the triangle formed by the normal to the curve $$x=e^{\sin y}$$ at (1, 0) with the coordinate axes is

The distance of the origin from the normal to the curve  $$y=e^{2x}+x^{2}$$ at $$x=0$$ is

The arrangment of the slopes of the normals to the curve  $$y=e^{\log(cosx)}$$ in the ascending order at the points given below.
$$A) \displaystyle x=\frac{\pi}{6},  B) \displaystyle x=\frac{7\pi}{4},  C)x=\frac{11\pi}{6},  D)x=\frac{\pi}{3}$$

lf the normal at the point $$p(\theta)$$ of the curve $$x^{\tfrac{2}{3}}+y^{\tfrac{2}{3}}=a^{\tfrac{2}{3}}$$ passes through the origin then

The equations of the tangents at the origin to the curve  $$y^{2}=x^{2}(1+x)$$ are

The equation of the common normal at the point of contact of the curves $$x^{2}=y$$ and $$x^{2}+y^{2}-8y=0$$