If each line of a pair of lines passing throu | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let the equation of a line passing through the origin with slope $m$ be $y - mx = 0$,or $mx - y = 0$. According to the given information,the perpe

Vedclass · Accepted Answer

$7y^2 + 24xy = 0$

Vedclass · Answer

(B) Let the equation of a line passing through the origin with slope $m$ be $y - mx = 0$,or $mx - y = 0$. According to the given information,the perpendicular distance from the point $(3, 4)$ to the line is $4$ units. Using the distance formula: $\frac{|m(3) - 1(4)|}{\sqrt{m^2 + (-1)^2}} = 4$. Squaring both sides: $\frac{(3m - 4)^2}{m^2 + 1} = 16$. $9m^2 - 24m + 16 = 16m^2 + 16$. $7m^2 + 24m = 0$. $m(7m + 24) = 0$,so $m = 0$ or $m = -\frac{24}{7}$. The equations of the lines are $y = 0$ and $y = -\frac{24}{7}x$,which is $7y + 24x = 0$. The combined equation is $y(7y + 24x) = 0$,which simplifies to $7y^2 + 24xy = 0$. Thus,option $B$ is correct.

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

Similar Questions

The value of $\lambda$ for which the equation $x^2 - \lambda xy + 2y^2 + 3x - 5y + 2 = 0$ represents a pair of straight lines is

For what value of $k$ does the equation $kx^2 - 10xy + 12y^2 + 5x - 16y - 3 = 0$ represent a pair of straight lines?

The equation $r^2 \cos^2 \left(\theta - \frac{\pi}{3}\right) = 2$ represents

If the equation of the pair of lines passing through $(1, 1)$ and perpendicular to the pair of lines $2x^2 + xy - y^2 - x + 2y - 1 = 0$ is $ax^2 + 2hxy + by^2 + 2gx + 3y = 0$,then $\frac{b}{a} =$

If the sum of the slopes of the lines represented by $x^2 - 2xy \tan \theta - y^2 = 0$ is $4$,then $\theta =$

Vedclass Test Series

Exam Paper Generator

Online Exam Module