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 $\ldots$

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