Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Advanced 2008Paper 1
Exam
JEE Advanced
Year
2008
Paper
Paper 1
Subject
Mathematics
Chapter
Pair of Lines

JEE Advanced 2008 · Paper 1 · Mathematics · Pair of Lines

Let a and b be non-zero and real numbers. Then, the equation (a...

Let aandba and b be non-zero and real numbers. Then, the equation \left(a x^2+b y^2+c\right)(x2−5xy+6y2)=0\left(x^2-5 x y+6 y^2\right)=0 represents

Options

  1. AFour straight lines, when c=0c=0 and a,ba, b are of the same sign
  2. BTwo straight lines and a circle, when a=ba=b and cc is of sign opposite to that of aa
  3. CTwo straight lines and a hyperbola, when aa and bb are of the same sign and cc is of sign opposite to that of aa
  4. DA circle and an ellipse, when aa and bb are of the same sign and cc is of sign opposite to that of aa

Correct answer

B. Two straight lines and a circle, when a=ba=b and cc is of sign opposite to that of aa

Step-by-step solution

Let aa and bb be non- zero real numbers. Therefore, the given equation (ax2+by2+c)(x2−5xy+6y2)=0\left(a x^2+b y^2+c\right)\left(x^2-5 x y+6 y^2\right)=0 implies either x2−5xy+6y2=0⇒(x−2y)(x−3y)=0⇒x=2y and x=3y\begin{array}{rc}& x²-5 x y+6 y²=0 \\ \Rightarrow & (x-2 y)(x-3 y)=0 \\ \Rightarrow & x=2 y \text{ and }x=3 y \end{array}represent two straight lines passing through origin. Or ax2+by2+c=0\quad a x^2+b y^2+c=0 When c=0c=0 and aa and bb are of same signs, then ax2+by2+c=0⇒x=0 and y=0\begin{aligned}& a x²+b y²+c=0 \\ \Rightarrow & x=0 \text{ and }y=0 \end{aligned}which is a point specified as the origin. When a=ba=b and cc is of sign opposite to that of a,ax2+by2+c=0a, a x^2+b y^2+c=0 represents a circle. Hence, the given equation (ax2+by2+c)(x2−5xy+6y2)=0\left(a x^2+b y^2+c\right)\left(x^2-5 x y+6 y^2\right)=0 may represent two straight lines and a circle.
Practice Pair of Lines on Quantrex Academy →

More from Pair of Lines

Let S denote the locus of the point of intersection of the pair of lines 4 x-3 y=12 α 4 α… JEE Advanced 2025 Full Pair of Lines list Pair of Lines JEE Maths PYQsJEE Mathematics PYQs All JEE Advanced PYQs