Find the length of the intercept cut by the pair of lines $2 x^2+4 x y-4 y^2-6 x-8 y+7=0$ over the $Y$-axis
Find the length of the intercept cut by the pair of lines $2 x^2+4 x y-4 y^2-6 x-8 y+7=0$ over the $Y$-axis
- $\sqrt{12}$
- $\sqrt{10}$
- $\sqrt{11}$
- $\sqrt{13}$
Solution
Given, pairs of straight line
$2 x^2+4 x y-4 y^2-6 x-8 y+7=0$
For length of intercept on $Y$-axis put $x=0$
$-4 y^2-8 y+7=0 \Rightarrow 4 y^2+8 y-7=0$
$y=\frac{-8 \pm \sqrt{64+112}}{8}$
$y=\frac{-8 \pm 4 \sqrt{11}}{8}$
Length of intercept
$=\frac{2 \times 4}{8} \sqrt{11}=\sqrt{11}$
Asked in: AP EAMCET 2021 (24 Aug Shift 2)
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