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The triangle formed by the pair of lines $2 x^{2} + 4 xy + 2 y^{2} = 0$ and the line $x + 2 y + 3 = 0$ is

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Equilateral

Isosceles

Right-angled

Does not exist

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detailed solution

Correct option is D

The given equation is 2x2+4xy+y2=0Observing the equation a=2,h=2,b=2It implies h2=abThe pair of lines represent coincide lines. Then triangle does not exist.

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The triangle formed by the pair of lines 2x2+4xy+2y2=0 and the line x+2y+3=0 is

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The triangle formed by the pair of lines $2 x^{2} + 4 xy + 2 y^{2} = 0$ and the line $x + 2 y + 3 = 0$ is