Let $f_k(x) = \dfrac{1}{k}(\cos^k x + \sin^k x)$ where $k \in N$, then $f_6(x) - f_4(x) = \ldots$

The coordinates of the orthocenter of the triangle whose sides are represented by the lines $4x - 7y + 10 = 0$, $x + y = 5$ and $7x + 4y = 15$ are $\ldots$

The combined equation of lines parallel to the coordinate axes and passing through the point of intersection of lines represented by $x^2 - 6xy + 5y^2 + 10x - 14y + 9 = 0$ is $\ldots$

The number of circles passing through the origin and touching the lines $x + y = 1$ and $x - y = 1$ is $\ldots$