The equation 8 x²-24 x y+18 y²-6 x+9 y-5=0 represents a _______

Correct Answer is : pair of parallel lines

Correct Answer is : pair of parallel lines

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AP EAPCET 19-Aug-2021 Shift 2 Paper

Section: Mathematics

Question : 47 of 160

Marks: +1, -0

The equation

8 x^{2}-24 x y+18 y^{2}-6 x+9 y-5=0

represents a _______

Solution:

Comparing given cquation,

8 x^{2}-24 x y+18 y^{2}-6 x+9 y-5=0

On comparing with general form

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

a=8, h=-12, b=18, g=-3, f=\frac{9}{2}, c=-5

\because h^{2}=144

and

a b=8 \times 18=144

\Rightarrow h^{2}=a b

and

a f^{2}=8\left(\frac{9}{2}\right)^{2}=8 \times \frac{81}{4}=2 \times 81=162

b g^{2}=18(-3)=18 \times 9=162

\Rightarrow a f^{2}=b g^{2}

\because h^{2}=a b

and

a f^{2}=b g^{2}

∴ Given pair of lines are parallel.

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