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A circle has the equation x2+10x+y2+9=0. What is its center?

Updated 6 days ago:

x^2+10x+y^2+9=0.

9 Answers

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  • 4 days ago

    x^2+10x+y^2+9=0

    =>

    x^2+10x+(10/2)^2-(10/2)^2+y^2+9=0

    =>

    (x+5)^2+(y+0)^2-25+9=0

    =>

    (x+5)^2+(y+0)^2=16

    =>

    the center of this circle is (-5,0)

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  • 6 days ago

    do complete the square for x and for y

    (x^2 +10x + 25) + y^2 = 25 - 9

    ==> (x+5)^2 +y^2 = 16

    so centre is (-5,0) and radius 4 units.

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  • Philip
    Lv 6
    6 days ago

    x^2 +10x +y^2 + 9 = 0. Completing the square gives x^2+10x+25 + y^2 = 4^2, ie., 

    (x+5)^2 + (y-0)^2 = 4^2, which defines a circle, radius 4, center (-5,0). 

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  • sepia
    Lv 7
    6 days ago

    A  circle has the equation x^2 + 10x + y^2 + 9 = 0. 

    circle

    center | (-5, 0)

    radius | 4

    diameter | 8

    area enclosed | 16 π≈50.2655

    circumference | 8 π≈25.1327

    centroid | (-5, 0)

    curvature | 1/4 = 0.25

    Its center is (-5, 0)

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  • 6 days ago

    Complete the Square in each letter

    (x + 5)^2 - (5)^2 =>

    (x + 5)^2 = 25

    Hence x = -5

    Since there are no terms in 'y' then y = 0

    Hence centre is (-5,0)

    the radius is

    -9 + 25 = 16

    radius = 4

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  • 6 days ago

    x² + 10x + y² + 9 = 0

    so, (x + 5)² + y² + 9 = 25

    Hence, (x + 5)² + y² = 16 => 4² 

    i.e. centre (-5, 0) and radius 4

    A sketch is below.

    :)>

    Attachment image
  • Pope
    Lv 7
    6 days ago

    Any circle in the plan can be written in this general form:

    x² + y² + Dx + Ey + F = 0

    If it is in fact a circle, its radius is (-D/2, -E/2).

    In your case, D = 10, E = 0, so (-5, 0) is the center.

    You should also check the radius though.

    radius = √(D² + E² - 4F)/2

    Look at the radicand.

    If D² + E² - 4F < 0, the equation has no solutions in the plane.

    If D² + E² - 4F = 0, then the locus is only a single point. See the center.

    If D² + E² - 4F > 0, then yes, it is a circle.

    For your case:

    D² + E² - 4F = (10)² + (0)² - 4(9) = 64

    It is a circle with center(-5, 0) and radius 4.

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  • 6 days ago

    x^2+10x+y^2+9=0

    x^2 + 10x + y^2 = - 9

    (x^2 + 10x + 25) + y^2 = - 9 + 25

    (x + 5)^2 + y^2 =√(16)

    (x + 5)^2 + y^2 = 4

    the center of the circle is (-5,0) answer//

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  • david
    Lv 7
    6 days ago

    compete the square .. twice

    x^2+10x+y^2+9=0.

    (x + 5)^2  +  (y + 0)^2 = 16

      center = (-5, 0)

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