Mathematics

Gates

15 March, 22:20

A circle has the equation 2x2+12x+2y2-16y-150=0.

Jerene must convert the equation to standard form. She writes a description of the steps she can take to convert the equation, but she is missing some information.

Step 1: Divide each term by 2 so that the coefficient of x2 and y2 will be 1.

Step 2: Add _[blank 1]_ to both sides.

Step 3: Add _[blank 2]_ to both sides to complete the square for the x's.

Step 4: Add _[blank 3]_ to both sides to complete the square for the y's.

Step 5: Factor the trinomial of the x's and rewrite as a perfect square, _[blank 4]_.

Step 6: Factor the trinomial of the y's and rewrite as a perfect square, _[blank 5]_.

Step 7: The standard form of the equation is _[blank 6]_.

Match each numbered blank to the answer that correctly fills the corresponding blank in the proof.