The area of the triangle formed by the co-ordinate axes and a tangent to the curve $x y=\mathrm{a}^2$ at the point $\left(x_1, y_1\right)$ is _______ sq. units (where a, $x_1$ and $y_1$ are non-zero)

The co-ordinates of the point in which line joining $(1,1,1)$ and $(2,2,2)$ intersects the plane $x+y+\mathrm{z}=9$ are

The minimum value of the slope of the tangent to curve $y=x^3-3 x^2+2 x+93$ is

If $\quad f(x)=\left\{\begin{array}{cc}\frac{9^x-2 \cdot 3^x+1}{\log (1+3 x) \cdot \tan 2 x} & , \text { if } x \neq 0 \\ a(\log b)^c & , \text { if } x=0\end{array}\right.$ is continuous at $x=0$, then $\mathrm{a}+\mathrm{b}+\mathrm{c}=$