Which of the following is the equation of a hyperbola?

Question

Which of the following is the equation of a hyperbola? (A) x2 - 4x + 16y + 17 = 0 (B) 4x2 + 4y2 - 16x + 4y -60 = 0 (C) x2 + 2y2 + 4x + 2y -27 = 0 (D) x2 - y2 + 3x - 2y -43 = 0

Tardigrade Admin · Accepted Answer

x2-y2+3 x-2 y-43=0 =(x+(3/2))2-(y+1)2-(5/4)-43=0 =(x+(3/2))2-(y+1)2=(177/4) =((x+(3/2))2/(177)4)-((y+1)2/(177)4)=1 It is hyperbola equation.

Q. Which of the following is the equation of a hyperbola?

$x^{2} - 4 x + 16 y + 17 = 0$

$4 x^{2} + 4 y 2 - 16 x + 4 y - 60 = 0$

$x^{2} + 2 y^{2} + 4 x + 2 y - 27 = 0$

$x^{2} - y^{2} + 3 x - 2 y - 43 = 0$

$x^{2} + 4 x + 6 y - 2 = 0$

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

Q. Which of the following is the equation of a hyperbola?

x2−4x+16y+17=0

4x2+4y2−16x+4y−60=0

x2+2y2+4x+2y−27=0

x2−y2+3x−2y−43=0

x2+4x+6y−2=0