Question

If each line of a pair of lines passing through origin is at a perpendicular distance of $4$ units from the point $(3, 4)$, then the equation of the pair of lines is

• A. $7x^2 + 24xy = 0$
• B. $7y^2 + 24xy = 0$
• C. $7y^2 - 24xy = 0$
• D. $7x^2 - 24xy = 0$

Answer 1

Answer: (B)

$7y^2 + 24xy = 0$

Answer 2

Let equation of line passes through origin having slope $m$ is $y-m x=0$, according to given information
$\frac{|4-3 m|}{\sqrt{1+m^{2}}}=4$
$\Rightarrow 16+9 m^{2}-24 m=16+16 m^{2}$
$\Rightarrow 7 m^{2}+24 m=0$
$\Rightarrow m=0$ or $m=-\frac{24}{7}$
so combined equation of required lines
$y\left(y+\frac{24}{7} x\right)=0$
$\Rightarrow 7 y^{2}+24 x y=0$