Mathematics
Grade9
Easy

Question

What is the standard equation when the center is (-1, -1) and the point on the circle is (4, -5)?

  1. left parenthesis x plus 1 right parenthesis squared plus left parenthesis y plus 1 right parenthesis squared equals 1
  2. left parenthesis x plus 1 right parenthesis squared plus left parenthesis y plus 1 right parenthesis squared equals square root of 43
  3. left parenthesis x plus 1 right parenthesis squared plus left parenthesis y plus 1 right parenthesis squared equals 41
  4. left parenthesis x plus 1 right parenthesis squared plus left parenthesis y plus 1 right parenthesis squared equals 5

hintHint:

The radius of circle is the distance between center of circle and any point on the circle. Using distance between two points formula find radius.  

The correct answer is: left parenthesis x plus 1 right parenthesis squared plus left parenthesis y plus 1 right parenthesis squared equals 41


    If there are two points left parenthesis x subscript 1 comma y subscript 1 right parenthesis and left parenthesis x subscript 2 comma y subscript 2 right parenthesis ,then distance between two points is

    Error converting from MathML to accessible text.
    Distance between the center  (-1, -1) and the point on the circle (4, -5) is equal to radius
    Radius (r) equals square root of left parenthesis 4 minus left parenthesis negative 1 right parenthesis right parenthesis squared plus left parenthesis negative 5 minus left parenthesis negative 1 right parenthesis right parenthesis squared end root
    equals square root of left parenthesis 5 right parenthesis squared plus left parenthesis negative 4 right parenthesis squared end root
equals square root of 25 plus 16 end root
equals square root of 41
    Equation of a circle whose centre is (h, k) and radius is r is left parenthesis x minus h right parenthesis squared plus left parenthesis y minus k right parenthesis squared equals r squared
    left parenthesis x minus left parenthesis negative 1 right parenthesis right parenthesis squared plus left parenthesis y minus left parenthesis negative 1 right parenthesis right parenthesis squared equals left parenthesis square root of 41 right parenthesis squared
left parenthesis x plus 1 right parenthesis squared plus left parenthesis y plus 1 right parenthesis squared equals 41
    Therefore, The standard equation of the circle is left parenthesis x plus 1 right parenthesis squared plus left parenthesis y plus 1 right parenthesis squared equals 41

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