The greatest slope among the lines represented by the equation $4 x^{2} - y^{2} + 2 y - 1 = 0$ is -

- 3

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Solution

The correct option is C $2$
$4 x^{2} - y^{2} + 2 y - 1 = 0$
$y^{2} - 2 y + 1 = 4 x^{2}$
${(y - 1)}^{2} = {(2 x)}^{2}$
$y - 1 = \pm 2 x$
$y = 2 x + 1 or y = - 2 x + 1$
Comparing the above equations with $y = m x + c$ , we have
Slope $(m) = 2, - 2$
Hence the greatest slope will be $2$ .

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