Rectangular Cartesian Coordinate System

Q.

Find the length of the perpendicular from the point $(x^1,y^1)$ to the straight line Ax + By + C = 0, the axes being inclined at an angle $\omega$, and the equation being written such that C is a negative quantity.

1. $\frac{A{x}^1+B{y}^1+C}{\sqrt{A^2+B^2}}.cos\omega$

2. $\frac{A{x}^1+B{y}^1+C}{\sqrt{A^2+B^2}}.sin\omega$

3. $\frac{A{x}^1+B{y}^1+C}{\sqrt{A^2+B^2-2ABsin\omega }}.cos\omega$

4. $\frac{A{x}^1+B{y}^1+C}{\sqrt{A^2+B^2-2ABcos\omega }}.sin\omega$

Q. If p be the measure of perpendicular segment from the origin on the line whose intercepts on the axes are 'a' and 'b', then which of the following is/are correct?

1. $\frac{1}{a^2}=\frac{1}{p^2}+\frac{1}{b^2}$
2. $\frac{1}{p^2}=\frac{1}{a^2}+\frac{1}{b^2}$
3. $p^2(a^2+b^2)=a^2{b}^2$
4. $p^2\left(a^2{b}^2\right)=a^2+b^2$