Convert the equation to the standard form for a hyperbola by completing the square on x and y.
-$$x ^ { 2 } - y ^ { 2 } + 6 x - 2 y + 7 = 0$$
A) $( x + 3 ) ^ { 2 } - ( y + 1 ) ^ { 2 } = 1$
B) $( y + 3 ) ^ { 2 } - ( x + 1 ) ^ { 2 } = 1$
C) $( x + 3 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = 1$
D) $\frac { ( y + 3 ) ^ { 2 } } { 4 } - \frac { ( x + 1 ) ^ { 2 } } { 36 } = 1$

Question

Quizplus · Accepted Answer

To convert the given equation to the standard form of a hyperbola by completing the square, we first organize the equation by terms and complete the square for both $x$ and $y$:$$x^2 - y^2 + 6x - 2y + 7 = 0$$Rearrange the equation:$$x^2 + 6x - y^2 - 2y = -7$$Complete the square for $x$ and $y$:$$x^2 + 6x + 9 - y^2 - 2y - 1 = -7 + 9 - 1$$$$x^2 + 6x + 9 - (y^2 + 2y + 1) = 1$$$$(x + 3)^2 - (y + 1)^2 = 1$$This matches option A.

Convert the Equation to the Standard Form for a Hyperbola x2−y2+6x−2y+7=0x ^ { 2 } - y ^ { 2 } + 6 x - 2 y + 7 = 0x2−y2+6x−2y+7=0

Convert the Equation to the Standard Form for a Hyperbola $x ^ { 2 } - y ^ { 2 } + 6 x - 2 y + 7 = 0$