Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
BITSAT 2016
Exam
BITSAT
Year
2016
Subject
Mathematics
Chapter
Pair of Lines

BITSAT 2016 · Mathematics · Pair of Lines

The equation x^ 2 -2 3 x y+3 y^ 2 -3 x+3 3 y-4=0 represents

The equation x2−23xy+3y2−3x+33y−4=0x^{2}-2 \sqrt{3} x y+3 y^{2}-3 x+3 \sqrt{3} y-4=0 \quad represents

Options

  1. Aa pair of intersecting lines
  2. Ba pair of parallel lines with distance between them 52\frac{5}{2}
  3. Ca pair of parallel lines with distance between them 525 \sqrt{2}
  4. Da conic section, which is not a pair of straight lines

Correct answer

B. a pair of parallel lines with distance between them 52\frac{5}{2}

Step-by-step solution

We have a=1,h=−3,b=3,g=−32a=1, h=-\sqrt{3}, b=3, g=-\frac{3}{2}, f=332,c=−4\mathrm{f}=\frac{3 \sqrt{3}}{2}, \mathrm{c}=-4 Thus abc+2fgh−af2−bg2−ch2=0a b c+2 f g h-a f^{2}-b g^{2}-c h^{2}=0 Hence the equation represents a pair of straight lines. Again ah=hb=gf=−13∴\frac{\mathrm{a}}{\mathrm{h}}=\frac{\mathrm{h}}{\mathrm{b}}=\frac{\mathrm{g}}{\mathrm{f}}=-\frac{1}{\sqrt{3}}\therefore the lines are parallel. The distance between them =2 g2−aca(a+b)=294+41(1+3)=52\sqrt{\frac{g^{2}-a c}{a(a+b)}}=2 \sqrt{\frac{\frac{9}{4}+4}{1(1+3)}}=\frac{5}{2}
Practice Pair of Lines on Quantrex Academy →

More from Pair of Lines

A(3,2,0), B(5,3,2), C(-9,6,-3) are three points forming a triangle. AD , the bisector of… BITSAT 2024Statement- 1 : If the general equation x^ 2 +y^ 2 +2 x y+2 g x+2 f y+4=0 represents a… BITSAT 2020If ∫_0^n[x] dx= 66 , then n= BITSAT 2009 Full Pair of Lines list Pair of Lines JEE Maths PYQsJEE Mathematics PYQs All BITSAT PYQs