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 $\ldots$

A parabola has its focus on the positive X-axis and the Y-axis as its directrix. If $P(\alpha , 4)$ is a point on this parabola such that the tangent to the parabola at point P passes through the origin, then the distance of P from origin is

If $\lim\limits_{x \to k} \dfrac{x^3 - k^3}{x^2 - k^2} = \lim\limits_{x \to 0} \dfrac{1 - \cos(2x)}{x \sin x}$, then the value of $k$ is $\ldots$