Question

The foci of the hyperbola $x^2-y^2-4x+10y-22=0$ are

• A. $(\pm 2+\sqrt{2},5)$
• B. $(2\pm \sqrt{2},5)$
• C. $(\pm 3+\sqrt{2},5)$
• D. $(\pm 4+\sqrt{2},5)$

Answer 1

Answer: (B)

$(2\pm \sqrt{2},5)$

$x^2-y^2-4x+10y-22=0$
$\Rightarrow (x^2-4x)-(y^2-10y)=22$
$\Rightarrow (x^2-4x+4)-(y^2-10y+25)=22+4-25=1$
$\Rightarrow (x-2{)}^2-(y-5{)}^2=1$
$\Rightarrow a^2=1,b^2=1,e=\sqrt{1+\frac{b^2}{a^2}}=\sqrt{2}$
Therefore foci are, $(x-2)=\pm ae=\pm \sqrt{2},y-5=0$
$\Rightarrow S\equiv (2\pm \sqrt{2},5)$
Hence, option 'B' is correct