JEE Main 2014 · 12 Apr · Shift 1 · Mathematics Q79

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MathematicsSingle correct+4 / -1Question 79 of 90

If the three distinct lines $x+2ay+a=0$ , $x+3by+b=0$ and $x+4ay+a=0$ are concurrent, then the point (a, b) lies on a :

circle

hyperbola

straight line

parabola

Answer and worked solution

Official answer: C

$\begin{vmatrix}1&2a&a\\1&3b&b\\1&4a&a\end{vmatrix}=0.$
Subtracting $R_1$ from $R_2$ and $R_3$ and expanding gives $-2a(b-a)=0$ . With $a\ne0$ (else lines 1 and 3 coincide), $a=b$ : the point lies on the straight line $y=x$ .

Topics:Family of lines and pair of lines Determinants and properties

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JEE Main 2014 · 12 Apr · Shift 1, Mathematics question 79