Pair of straight lines

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If the slope of one line of the pair of lines represented by ${ax}^{2} + 10 xy + y^{2} = 0$ is four times the slope of the other, then a is equal to

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Solution

If $m_{1}, m_{2}$ are the slopes of two lines whose combined equation is ${ax}^{2} + 2 hxy + {by}^{2} = 0$ then the relation between the slopes and the coefficients of equation are $m_{1} + m_{2} = - \frac{2 h}{b}, m_{1} m_{2} = \frac{a}{b}$
Since the slopes of the lines represented by the equation ${ax}^{2} + 10 xy + y^{2} = 0$ are one is four times of the other.
Hence, $m + 4 m = 10 \Rightarrow m = - 2$ and $m \cdot 4 m = a \Rightarrow a = 16$
Therefore, $a = 16$

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Pair of straight lines

Remember concepts with our Masterclasses.

If the slope of one line of the pair of lines represented by ax2+10xy+y2=0 is four times the slope of the other, then a is equal to

Ready to Test Your Skills?

free study material

If the slope of one line of the pair of lines represented by ${ax}^{2} + 10 xy + y^{2} = 0$ is four times the slope of the other, then a is equal to