The equation {y^2} - {x^2} + 2x - 1 = 0 repre | vedclass

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(C) Given equation is ${y^2} - {x^2} + 2x - 1 = 0$.Comparing the given equation with the general second-degree equation $ax^2 + 2hxy + by^2 + 2gx + 2f

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$A$ pair of straight lines

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(C) Given equation is ${y^2} - {x^2} + 2x - 1 = 0$.Comparing the given equation with the general second-degree equation $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$,we get:$a = -1, h = 0, b = 1, g = 1, f = 0, c = -1$.The condition for the equation to represent a pair of straight lines is the determinant $\Delta = 0$,where $\Delta = abc + 2fgh - af^2 - bg^2 - ch^2$.Substituting the values:$\Delta = (-1)(1)(-1) + 2(0)(1)(0) - (-1)(0)^2 - (1)(1)^2 - (-1)(0)^2$$\Delta = 1 + 0 - 0 - 1 - 0 = 0$.Since $\Delta = 0$,the equation represents a pair of straight lines.

The equation ${y^2} - {x^2} + 2x - 1 = 0$ represents

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