(A) The given equation is ${y^2} - ({x^2} - 2x + 1) = 0$.This can be rewritten as ${y^2} - {(x - 1)^2} = 0$.Using the identity ${a^2} - {b^2} = (a - b

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(A) The given equation is ${y^2} - ({x^2} - 2x + 1) = 0$.This can be rewritten as ${y^2} - {(x - 1)^2} = 0$.Using the identity ${a^2} - {b^2} = (a - b)(a + b)$,we get $(y - (x - 1))(y + (x - 1)) = 0$.This simplifies to $(y - x + 1)(y + x - 1) = 0$.Since the equation can be factored into two linear equations,it represents a pair of straight lines.

Class 11 Mathematics Pair of straight lines Equation of pair of straight lines

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

A
$A$ pair of straight lines
B
$A$ circle
C
$A$ parabola
D
An ellipse

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Pair of straight lines

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Equation of pair of straight lines

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

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