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1 February, 02:16

Match the pairs of equations that represent concentric circles.

3x2 + 3y2 + 12x - 6y - 21 = 0

5x2 + 5y2 - 10x + 40y - 75 = 0

5x2 + 5y2 - 30x + 20y - 10 = 0

4x2 + 4y2 + 16x - 8y - 308 = 0

x2 + y2 - 12x - 8y - 100 = 0

2x2 + 2y2 - 8x + 12y - 40 = 0

4x2 + 4y2 - 16x + 24y - 28 = 0

3x2 + 3y2 - 18x + 12y - 81 = 0

x2 + y2 - 2x + 8y - 13 = 0

x2 + y2 + 24x + 30y + 17 = 0

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Answers (1)
  1. 1 February, 04:30
    0
    3x^2 + 3y^2 + 12x - 6y - 21 = 0 = > x^2 + y^2 + 4x - 2y - 7 = 0 = > x^2 + 4x + 4 + y^2 - 2y + 1 = 12 = > (x + 2) ^2 + (y - 1) ^2 = 12 = > centre is (-2, 1)

    5x^2 + 5y^2 - 10x + 40y - 75 = 0 = > x^2 + y^2 - 2x + 8y - 15 = 0 = > x^2 - 2x + 1 + y^2 + 8y + 16 = 32 = > (x - 1) ^2 + (y + 4) ^2 = 32 = > centre is (1, - 4)

    5x^2 + 5y^2 - 30x + 20y - 10 = 0 = > x^2 + y^2 - 6x + 4y - 2 = 0 = > x^2 - 6x + 9 + y^2 + 4y + 4 = 15 = > (x - 3) ^2 + (y + 2) ^2 = 15 = > centre is (3, - 2)

    4x^2 + 4y^2 + 16x - 8y - 308 = 0 = > x^2 + y^2 + 4x - 2y - 77 = 0 = > x^2 + 4x + 4 + y^2 - 2y + 1 = 82 = > (x + 2) ^2 + (y - 1) ^2 = 82 = > centre is (-2, 1)

    x^2 + y^2 - 12x - 8y - 100 = 0 = > x^2 - 12x + 36 + y^2 - 8y + 16 = 152 = > (x - 6) ^2 + (y - 4) ^2 = 152 = > centre is (6, 4)

    2x^2 + 2y^2 - 8x + 12y - 40 = 0 = > x^2 + y^2 - 4x + 6y - 20 = 0 = > x^2 - 4x + 4 + y^2 + 6y + 9 = 33 = > (x - 2) ^2 + (y + 3) ^2 = 33 = > centre is (2, - 3)

    4x^2 + 4y^2 - 16x + 24y - 28 = 0 = > x^2 + y^2 - 4x + 6y - 7 = 0 = > x^2 - 4x + 4 + y^2 + 6y + 9 = 20 = > (x - 2) ^2 + (y + 3) ^2 = 20 = > centre is (2, - 3)

    3x^2 + 3y^2 - 18x + 12y - 81 = 0 = > x^2 + y^2 - 6x + 4y - 27 = 0 = > x^2 - 6x + 9 + y^2 + 4y + 4 = 40 = > (x - 3) ^2 + (y + 2) ^2 = 40 = > centre is (3, - 2)

    x^2 + y^2 - 2x + 8y - 13 = 0 = > x^2 - 2x + 1 + y^2 + 8y + 16 = 30 = > (x - 1) ^2 + (y + 4) ^2 = 30 = > centre = (1, - 4)

    x^2 + y^2 + 24x + 30y + 17 = 0 = > x^2 + 24x + 144 + y^2 + 30y + 225 = 352 = > (x + 12) ^2 + (y + 15) ^2 = 352 = > center is (-12, - 15)

    Therefore, 3x^2 + 3y^2 + 12x - 6y - 21 = 0 and 4x^2 + 4y^2 + 16x - 8y - 308 = 0 are concentric.

    5x^2 + 5y^2 - 10x + 40y - 75 = 0 and x^2 + y^2 - 2x + 8y - 13 = 0 are concentric.

    5x^2 + 5y^2 - 30x + 20y - 10 = 0 and 3x^2 + 3y^2 - 18x + 12y - 81 = 0 are concentric.

    2x^2 + 2y^2 - 8x + 12y - 40 = 0 and 4x^2 + 4y^2 - 16x + 24y - 28 = 0 are concentric.
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Home » Mathematics » Match the pairs of equations that represent concentric circles. 3x2 + 3y2 + 12x - 6y - 21 = 0 5x2 + 5y2 - 10x + 40y - 75 = 0 5x2 + 5y2 - 30x + 20y - 10 = 0 4x2 + 4y2 + 16x - 8y - 308 = 0 x2 + y2 - 12x - 8y - 100 = 0 2x2 + 2y2 - 8x + 12y - 40 =
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