Question

If the distance of two lines passing through origin from the point $(x_1,y_1)$ is 'd',then the equation of lines is

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

If the equation of line is y = mx and the length of perpendicular drawn on it from the point $(x_1,y_1)$ is d, then $\frac{y_1-m{x}_1}{\sqrt{1+m^2}}=\pm d\Rightarrow (y_1-m{x}_1{)}^2=d^2(1+m^2).$ But $m=\frac{y}{x}$, therefore on eliminating 'm', the required equation is $(x{y}_1-y{x}_1{)}^2=d^2(x^2+y^2)$.