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

- 3

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2

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Solution

The correct option is C $2$
4x²-y²+2y-1 = 0
⇒ 4x²-(y²-2y+1) = 0
⇒ 4x²-(y-1)² = 0
⇒ 4x² = (y-1)²
Taking square root,
This has the following two solutions:
y = -2x+1, with slope -2
y = 2x+1, with slope 2
Thus, greatest slope is 2.

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