Question

What is the equation of the curve y2−6y−12x−39=0 when expressed in standard form?

A. (y−3)2=12(x−4)
B.(y+3)2=12(x−4)
C. (y−3)2=12x−39
D. (y+3)2=12x−39

Answer 1

The standard form of the equation y²−6y−12x−39=0 is (y − 3)² = 12(x − 4) after completing the square, which corresponds to option A.

Step-by-step explanation:

To express the equation y²−6y−12x−39=0 in standard form, we need to complete the square for the variable y. First, we rearrange the equation:

y² − 6y = 12x + 39

Then we add (6/2)² = 9 to both sides to complete the square:

y² − 6y + 9 = 12x + 39 + 9

Simplify and write the left side as a square:

(y − 3)² = 12x + 48

Finally, we complete the square for x by isolating x to find the standard form:

(y − 3)² = 12(x − 4)

The correct answer in standard form is (y − 3)² = 12(x − 4), which corresponds to option A.