The equation $3 x^{2} - 8 x y - 3 y^{2} = 0$ and $x - 2 y = 3$ represents the sides of a triangle which is

equilateral

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isosceles

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right angled triangle

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none of these

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Solution

The correct option is B right angled triangle
Given equation of pair of lines $3 x^{2} - 8 x y - 3 y^{2} = 0$ ,
Let $\frac{y}{x} = m$ , we get $3 m^{2} + 8 m - 3 = 0$ Let $m_{1}$ and $m_{2}$ are slopes of lines,we get $m_{1} \times m_{2} = - 1$
$∴$ lines are perpendicular to each other.
Then triangle is Right angled triangle .

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The equation 3x2−8xy−3y2=0 and x−2y=3 represents the sides of a triangle which is

The correct option is B right angled triangleGiven equation of pair of lines 3x2−8xy−3y2=0,Let yx=m, we get 3m2+8m−3=0 Let m1 and m2 are slopes of lines,we get m1×m2=−1∴ lines are perpendicular to each other.Then triangle is Right angled triangle .

The equation $3 x^{2} - 8 x y - 3 y^{2} = 0$ and $x - 2 y = 3$ represents the sides of a triangle which is