Number of points of intersection of the hyperbolas $x^{2} - 2 x - y^{2} + 4 y - 4 = 0$ and $x^{2} - 2 x - y^{2} + 4 y - 2 = 0$ is/are

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Solution

$x^{2} - 2 x - y^{2} + 4 y - 4 = 0$ ........... $(i)$
$x^{2} - 2 x - y^{2} + 4 y - 2 = 0$ ........... $(i i)$
$(i) - (i i)$ , gives
$- 4 - (- 2) = 0$
$- 4 + 2 = 0$
$- 2 = 0$ which is false
Therefore, given hyperbola do not intersect each other at all
Therefore No. of points of intersection=0

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Number of points of intersection of the hyperbolas x2−2x−y2+4y−4=0 and x2−2x−y2+4y−2=0 is/are

x2−2x−y2+4y−4=0 ........... (i)x2−2x−y2+4y−2=0 ........... (ii)(i)−(ii), gives−4−(−2)=0−4+2=0−2=0 which is falseTherefore, given hyperbola do not intersect each other at allTherefore No. of points of intersection=0

Number of points of intersection of the hyperbolas $x^{2} - 2 x - y^{2} + 4 y - 4 = 0$ and $x^{2} - 2 x - y^{2} + 4 y - 2 = 0$ is/are

$x^{2} - 2 x - y^{2} + 4 y - 4 = 0$ ........... $(i)$
$x^{2} - 2 x - y^{2} + 4 y - 2 = 0$ ........... $(i i)$
$(i) - (i i)$ , gives
$- 4 - (- 2) = 0$
$- 4 + 2 = 0$
$- 2 = 0$ which is false
Therefore, given hyperbola do not intersect each other at all
Therefore No. of points of intersection=0