Multiple choice help

Question

To put the equation in standard form, what should you do first?
5x² - 3y² - 20x + 6y + 2 = 0

Select one:

a. Add all the coefficients to the zero term

b. Divide every term by the GCF of 5

c. Add the x terms together and add the y terms together.

d. Place similar terms with variables together one one side and numbers on the other to prepare for completing the square.

 

Answer 1

d is the answer.

5x² - 20x - 3y² + 6y +2 = 0

5(x² - 4x) - 3(y² - 2y) +2 = 0

To change the expression into a perfect square  add (half the x coefficient)² and (half the y - coeffient)² to each side of the expression.

Here x coefficient = - 4, so, (half the x coefficient)² = (- 4/2)²= 4.

Here y coefficient = - 2, so, (half the x coefficient)² = (- 2/2)²= 1.

Add 20 and - 3 to each side of the equation.

5(x² - 4x + 4) - 3(y² - 2y + 1)+2 = 0 + 20 - 3

5(x - 2)² - 3y - 1)² = - 2 + 17

5(x - 2)² - 3(y - 1)² = 15

(x - 2)²/3 - (y - 1)²/5= 1