Search any question & find its solution
Question:
Answered & Verified by Expert
The separate equations of the lines represented by the equation
$3 x^{2}-2 \sqrt{3} x y-3 y^{2}=0$ are
Options:
$3 x^{2}-2 \sqrt{3} x y-3 y^{2}=0$ are
Solution:
2404 Upvotes
Verified Answer
The correct answer is:
$x-\sqrt{3} y=0$ and $3 x+\sqrt{3} y=0$
$3 x^{2}-2 \sqrt{3} x y-3 y^{2}=0$
$3 x^{2}-3 \sqrt{3} x y+\sqrt{3} x y-3 y^{2}=0 \Rightarrow 3 x(x-\sqrt{3} y)+\sqrt{3} y(x-\sqrt{3} y)=0$
$(3 x+\sqrt{3} y)(x-\sqrt{3} y)=0 \Rightarrow 3 x+\sqrt{3} y=0, \quad x-\sqrt{3} y=0$
$3 x^{2}-3 \sqrt{3} x y+\sqrt{3} x y-3 y^{2}=0 \Rightarrow 3 x(x-\sqrt{3} y)+\sqrt{3} y(x-\sqrt{3} y)=0$
$(3 x+\sqrt{3} y)(x-\sqrt{3} y)=0 \Rightarrow 3 x+\sqrt{3} y=0, \quad x-\sqrt{3} y=0$
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.