2x^2 + 2y^2 – 8x + 10y + 2 =0 PLEASE help me with this problem. Rewrite in standard form. Find the center and radius of the circle. Sh

Question

2x^2 + 2y^2 – 8x + 10y + 2 =0
PLEASE help me with this problem. Rewrite in standard form. Find the center and radius of the circle. Show all of your work.

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RuslanHeatt 5 months 2021-08-10T20:35:33+00:00 1 Answers 14 views 0

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    2021-08-10T20:37:08+00:00

    A circle of radius r centered at (a, b) has equation

    (xa)² + (yb)² = r ²

    To get the given equation in this form, complete the square with respect to both x and y.

    2x² – 8x = 2 (x² – 4x)

    2x² – 8x = 2 (x² – 4x + 4 – 4)

    2x² – 8x = 2 ((x – 2)² – 4)

    2x² – 8x = 2 (x – 2)² – 8

    2y² + 10y = 2 (y² + 5y)

    2y² + 10y = 2 (y² + 5y + 25/4 – 25/4)

    2y² + 10y = 2 ((y + 5/2)² – 25/4)

    2y² + 10y = 2 (y + 5/2)² – 25/2

    So we have

    2x² + 2y² – 8x + 10y + 2 = 0

    2 (x – 2)² – 8 + 2 (y + 5/2)² – 25/2 + 2 = 0

    2 (x – 2)² + 2 (y + 5/2)² = 37/2

    (x – 2)² + (y + 5/2)² = 37/4

    (x – 2)² + (y + 5/2)² = ((√37)/2)²

    which means this circle has radius (√37)/2 and center (2, -5/2).

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Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )