Question

Which of the following is the equation of a hyperbola?

• A. $x^2 - 4x + 16y + 17 = 0$
• B. $4x^2 + 4y2 - 16x + 4y -60 = 0$
• C. $x^2 + 2y^2 + 4x + 2y -27 = 0$
• D. $x^2 - y^2 + 3x - 2y -43 = 0$
• E. $x^2 + 4x + 6y - 2 = 0$

Answer 1

Answer: (D)

$x^{2}-y^{2}+3 x-2 y-43=0$
$=\left(x+\frac{3}{2}\right)^{2}-(y+1)^{2}-\frac{5}{4}-43=0$
$=\left(x+\frac{3}{2}\right)^{2}-(y+1)^{2}=\frac{177}{4}$
$=\frac{\left(x+\frac{3}{2}\right)^{2}}{\frac{177}{4}}-\frac{(y+1)^{2}}{\frac{177}{4}}=1$
It is hyperbola equation.