The equation of a line passing through the intersection of lines $x = 0$ and $y = 0$ and through the point $(2, 2)$ is:

If the straight line $2x - 3y + 17 = 0$ is perpendicular to the line passing through the points $(7, 17)$ and $(15, \beta)$,then $\beta$ equals

The sum of the squares of the intercepts made by the line $5x - 2y = 10$ on the coordinate axes equals:

Find the equation of the line perpendicular to the line $x-7y+5=0$ and having $x$-intercept $3$.

If the $x-$intercept of some line $L$ is double that of the line $3x + 4y = 12$ and the $y-$intercept of $L$ is half that of the same line,then the slope of $L$ is

If the straight line passing through the point $P(3,4)$ makes an angle $\frac{\pi}{6}$ with the positive direction of $X$-axis and meets the line $12x + 5y + 10 = 0$ at $Q$,then the length of $PQ$ is