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)

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