Search any question & find its solution
Question:
Answered & Verified by Expert
The joint equation of the pair of lines through the origin and making an equilateral triangle with the line $x=3$ is
Options:
Solution:
1268 Upvotes
Verified Answer
The correct answer is:
$x^2-3 y^2=0$
Slope of line $\mathrm{OA}=\tan 30^{\circ}=\frac{1}{\sqrt{3}}$ and
Slope of line $\mathrm{OB}=\tan \left(-30^{\circ}\right)=\frac{-1}{\sqrt{3}}$
$\therefore$ Equation of $\mathrm{OA}$ is $\mathrm{y}=\frac{1}{\sqrt{3}} \mathrm{x}$ and equation of $\mathrm{OB}$ is $\mathrm{y}=\frac{1}{\sqrt{3}} \mathrm{x}$ Hence required equation is
$$
(x-\sqrt{3 y})(x+\sqrt{3 y})=0 \text { i.e. } x^2-3 y^2=0
$$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.