Convert the equation to the standard form for a parabola by completing the square on x or y as appropriate.
-$$y ^ { 2 } - 4 y - 6 x + 34 = 0$$
A) $( y - 2 ) ^ { 2 } = 6 ( x - 5 )$
B) $( y + 2 ) ^ { 2 } = 6 ( x - 5 )$
C) $( y + 2 ) ^ { 2 } = - 6 ( x - 5 )$
D) $( y - 2 ) ^ { 2 } = 6 ( x + 5 )$

Question

Quizplus · Accepted Answer

To convert the given equation $y^2 - 4y - 6x + 34 = 0$ to the standard form of a parabola by completing the square, we focus on the $y$ terms. First, isolate the $y$ terms and move the $x$ term to the other side: $y^2 - 4y = 6x - 34$. To complete the square, we take half of the coefficient of $y$ (which is $-4$), square it ($(-2)^2 = 4$), and add it to both sides, ensuring to maintain the equation's balance. This gives us $y^2 - 4y + 4 = 6x - 34 + 4$, simplifying to $(y - 2)^2 = 6(x - 5)$, which matches choice A.

Convert the Equation to the Standard Form for a Parabola y2−4y−6x+34=0y ^ { 2 } - 4 y - 6 x + 34 = 0y2−4y−6x+34=0

Convert the Equation to the Standard Form for a Parabola $y ^ { 2 } - 4 y - 6 x + 34 = 0$