Question

The perpendiculars that fall from any point of the straight line $2x+11y=5$ upon the two straight lines $24x+7y=20$ and $4x-3y=2$ are

• A. $12$ and $4$ respectively
• B. $11$ and $5$ respectively
• C. Equal to each other
• D. Not equal to each other

Answer 1

The correct option is C Equal to each other

As the given situation is for any point, it is easy to assume a point and then solve. So, for simplicity, let $y=0$ and hence, the required point is $(\frac{5}{2},0)$.

The length of perpendicular from $(\frac{5}{2},0)$ to $24x+7y-20=0$ is $\left|\frac{60+0-20}{\sqrt{{24}^2+7^2}}\right|=\frac{8}{5}$

Also,

The length of perpendicular from $(\frac{5}{2},0)$ to $4x-3y-2=0$ is $\left|\frac{10+0-2}{\sqrt{4^2+3^2}}\right|=\frac{8}{5}$

Hence, they are equal.