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Examine whether the equation x^(2) + y^(...

Examine whether the equation `x^(2) + y^(2) - x - 4y + 7 = 0` represents a circle.

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The correct Answer is:
Does not represent a real circle.
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Knowledge Check

  • The equation x^(3) - yx^(2) + x - y = 0 represents

    A
    a hyperbola and two straight lines
    B
    a straight line
    C
    a parabola and two straight lines
    D
    a straight line and a circle

  • The equation x^(2) + y^(2) + 2gx + 2fy + c = 0 represents a point-circle when -

    A
    `g^(2) + f^(2) = -c`
    B
    `g^(2) - f^(2) = -c`
    C
    `g^(2) + f^(2) = c`
    D
    `f^(2) - g^(2) = c`

  • If the equation (x^(2))/(4-m)+(y^(2))/(m-7)+ 1 = 0 represents an ellipse then _

    A
    `mlt 4 `
    B
    `m gt 7`
    C
    `m gt 7 or m lt 2 `
    D
    `4 lt m lt 7 `

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