The equation y^2 - x^2 + 2x - 1 = 0 represents - Vidyadip

MCQ

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

A
A hyperbola
B
An ellipse
✓
A pair of straight lines
D
A rectangular hyperbola

✓

Answer

Correct option: C.

A pair of straight lines

c
(c) Given equation is ${y^2} - {x^2} + 2x - 1 = 0$

Comparing the given equation with

$a{x^2} + 2hxy + b{y^2} + 2gx + 2fy + c = 0$

We get, $a = 1$, $h = 0$, $b = 1$, $g = 1$, $f = 0$, $c = - 1$

$\therefore $ $\Delta = abc + 2fgh - a{f^2} - b{g^2} - c{h^2}$

$\Delta = 1 + 0 + 0 - 1 = 0$

Hence, the given equation represents two straight lines.

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