The sum of slopes of lines $3 x^{2} + 5 x y - 2 y^{2} = 0$ is

- \frac{5}{3}

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\frac{5}{2}

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- \frac{5}{2}

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- \frac{2}{3}

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Solution

The correct option is B $\frac{5}{2}$
$3 x^{2} + 5 x y - 2 y^{2} = 0$
$3 x^{2} + 6 x y - x y - 2 y^{2} = 0 \Rightarrow 3 x (x + 2 y) - y (x + 2 y) = 0$
$\Rightarrow (3 x - y) (x + 2 y) = 0$
$L_{1}$ $L_{2}$
$L_{1} : 3 x - y = 0$ $L_{2} : x + 2 y = 0 \Rightarrow y = - x / 2$
$m_{1} = 3$ $m_{2} = - 1 / 2$
$m_{1} + m_{2} = 3 - \frac{1}{2} = \frac{5}{2}$

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Similar questions

The equations of the asymptotes of the hyperbola $2 x^{2} + 5 x y + 2 y^{2} - 11 x - 7 y - 4 = 0$ are

2 x^{2} + 5 x y + 2 y^{2} - 11 x - 7 y - 4 = 0

3 x^{2} + 2 y^{2} = 0, 4 x^{- 2} + 6 y = 5

Which of the following statement is / are correct for equation 2x - 3y + 5 = 0?

1. Slope of the straight line is $\frac{2}{3}$ .

2. x-intercept of the straight line is $\frac{- 5}{2}$ .

3. y-intercept of the straight line is $\frac{5}{3}$ .

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