If 4 x²+12 x y+9 y²+2 g x+2 f y-1=0 represent a pair of parallel lines, then

Correct Answer is : f/g+ g/f= 13/6\;{f}/{g}+\;{g}/{f}=\;{13}/{6}f/g+g/f=13/6

Correct Answer is : f/g+ g/f= 13/6\;{f}/{g}+\;{g}/{f}=\;{13}/{6}f/g+g/f=13/6

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TG EAMCET 2 May 2025 Shift 1 Paper

Question : 46 of 160

Marks: +1, -0

4 x^2+12 x y+9 y^2+2 g x+2 f y-1=0

Solution:

Given equation,

4 x^2+12 x y+9 y^2+2 g x+2 f y-1=0

Since, general second-degree equation

a x^2+2 h x y+b y^2+2 g x+2 f y+c=0

represents a pair of straight lines, if

\Delta= a b c+2 f g h-b g^2-c h^2-a f^2=0

Here,

a=4, b=9, h=6

So,

\Delta=4 \times 9 \times c+2 f g \times 6-9 g^2

\; -c(6)^2-4 f^2=0

\; =36 c+12 f g-9 g^2-36 c-4 f^2=0

\; =12 f g-9 g^2-4 f^2=0

\Rightarrow \; \; -(3 g-2 f)^2=0 \Rightarrow 3 g-2 f=0

\Rightarrow \; \frac{g}{f} \; = \; \frac{2}{3} \; \text{ and } \; \; \frac{f}{g} = \; \frac{3}{2}

So,

\; \frac{f}{g} + \; \frac{g}{f} + \; \frac{13}{6}=0

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