Consider the following statements

1. For an equation of a line, $$x\cos \theta + y\sin \theta = p$$, in normal form, the length of the perpendicular from the point ($$\alpha$$, $$\beta$$) to the line is $$\left| {\alpha \cos \theta + \beta \sin \theta + p} \right|$$.

The length of the perpendicular from the point ($$\alpha$$, $$\beta$$) to the line $${x \over a} + {y \over b} = 1$$ is $$\left| {{{a\alpha + b\beta - ab} \over {\sqrt {{a^2} + {b^2}} }}} \right|$$.

Which of the above statements is/are correct?

The points (1, 3) and (5, 1) are two opposite vertices of a rectangle. The other two vertices lie on the line y = 2x + c. What is the value of c?

If the lines 3y + 4x = 1, y = x + 5 and 5y + bx = 3 are concurrent, then what is the value of b?

What is the equation of the straight line which is perpendicular to y = x and passes through (3, 2) ?