Write the equation in standard form by filling in the square and indicate the conical section it represents. displaystyle{2}{x}^{2}+{2}{y}^{2}-{8}{x}-{8}{y}={0}

Question

Write the equation in standard form by filling in the square and indicate the conical section it represents.

2 x^{2} + 2 y^{2} - 8 x - 8 y = 0

Answer 1

Step 1

2 x^{2} + 2 y^{2} - 8 x - 8 y = 0

2 [x^{2} - 4 x] + 2 [y^{2} - 4 y] = 0

2 [{(x - 2)}^{2} - 4] + 2 [{(y - 2)}^{2} - 4] = 0

2 {(x - 2)}^{2} + 2 {(y - 2)}^{2} = 16

Step 2

{(x - 2)}^{2} + {(y - 2)}^{2} = 8

{(x - 2)}^{2} + {(y - 2)}^{2} = {(2 \sqrt{2})}^{2}

Answer:
This equation represents a circle centered at (2,2) and radius of

2 \sqrt{2}

Answer 2

Jeffrey Jordon

Answered 2021-10-26 Author has 2047 answers

Answer is given below (on video)

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