List of top Mathematics Questions on Various Forms of the Equation of a Line asked in MHT CET

The equation of line, where length of the perpendicular segment from origin to the line is 4 and the inclination of this perpendicular segment with the positive direction of X-axis is $30^\circ$, is

The equation of a line passing through $(p \cos \alpha, p \sin \alpha)$ and making an angle $(90 + \alpha)$ with positive direction of X-axis is

The x-intercept of a line passing through the points $\left(-\frac{1}{2}, 1\right)$ and $(1, 2)$ is :

If the lines $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}$ and $\frac{x-3}{1}=\frac{y-k}{2}=\frac{z}{1}$ intersect, then the value of $k$ is

The parametric equations of a line passing through the points $A(3,4,-7)$ and $B(1,-1,6)$ are

The equation of a line passing through $(p \cos \alpha, p \sin \alpha)$ and making an angle $(90 + \alpha)$ with positive direction of X-axis is