Pair of straight lines

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If the equation $2 x^{2} + 2 h x y + 6 y^{2} - 4 x + 5 y - 6 = 0$ represents a pair of straight lines, then the length of intercept on the $x$ -axis cut by the lines is equal to

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Solution

The $x$ -coordinates of the points of intersection of
the pair of lines given by $2 x^{2} + 2 h x y + 6 y^{2} - 4 x + 5 y - 6 = 0$ and
$x$ -axis are roots of the equation
$\begin{array}{l} 2 x^{2} - 4 x - 6 = 0 or, x^{2} - 2 x - 3 = 0 \\ \Rightarrow (x - 3) (x + 1) = 0 \Rightarrow x = - 1, 3 \end{array}$
Hence, required length $= |x_{1} - x_{2}| = 4,$

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Pair of straight lines

Remember concepts with our Masterclasses.

If the equation 2x2+2hxy+6y2−4x+5y−6=0 represents a pair of straight lines, then the length of intercept on the x-axis cut by the lines is equal to

The x-coordinates of the points of intersection ofthe pair of lines given by 2x2+2hxy+6y2−4x+5y−6=0 and x-axis are roots of the equation2x2−4x−6=0 or, x2−2x−3=0⇒ (x−3)(x+1)=0⇒x=−1, 3Hence, required length =x1−x2=4,

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If the equation $2 x^{2} + 2 h x y + 6 y^{2} - 4 x + 5 y - 6 = 0$ represents a pair of straight lines, then the length of intercept on the $x$ -axis cut by the lines is equal to