The equation $3 x^{2} - 8 x y - 3 y^{2} = 0$ and $x + 2 y = 3$ represent the sides of

an equilateral triangle

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isosceles triangle

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right angled triangle

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obtuse angled triangle

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Solution

The correct options are
A isosceles triangle
C right angled triangle
For $3 x^{2} - 8 x y - 3 y^{2} = 0$
Angle between then is $tan θ = \frac{2 \sqrt{h^{2} - a b}}{a + b} = \infty \Rightarrow θ = \frac{π}{2}$
and $3 x^{2} - 8 x y - 3 y^{2} = 0 \Rightarrow (x - 3 y) (3 x + y) = 0$
Hence line $x - 3 y = 0$ , $3 x + y = 0$ and $x + 2 y = 3$ for a isosceles right angle triangle

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