"Find the required information and graph: 2x2+2y2+2x+14y+17=0" was answered by our experts

ankarskogC

Answered question

2021-02-25

Find the required information and graph:

2 x^{2} + 2 y^{2} + 2 x + 14 y + 17 = 0

Nicole Conner

Skilled2021-02-26Added 97 answers

Step 1
Consider the provided equation,

2 x^{2} + 2 y^{2} + 2 x + 14 y + 17 = 0

Classify the conic section and find the center.
We can write as,

2 x^{2} + 2 x + 2 y^{2} + 14 y + 17 = 0

2 (x^{2} + x) + 2 (y^{2} + 7 y) = - 17

(x^{2} + x) + (y^{2} + 7 y) = - \frac{17}{2}

(x^{2} + x + \frac{1}{4}) + (y^{2} + 7 y + \frac{49}{4}) = - \frac{17}{2} + \frac{49}{4} + \frac{1}{4}

Step 2
Simplifying further,

{(x + \frac{1}{2})}^{2} + {(y + \frac{7}{2})}^{2} = 4

{(x - (- \frac{1}{2}))}^{2} + {(y - (- \frac{7}{2}))}^{2} = 2^{2}

{(x - a)}^{2} + {(y - b)}^{2} = r^{2}

is the circle equation with radius r, centered at (a, b).
Thus, this is a circle.
So, the center or the circle

(- \frac{1}{2}, - \frac{7}{2}) .

Jeffrey Jordon

Expert2021-10-26Added 2605 answers

Answer is given below (on video)

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