Mathematics
Grade9
Easy

Question

Write the standard equation of when the center is (0, 6) and point on the circle is (2, 3).

  1. x squared plus y squared equals 13
  2. x squared plus left parenthesis y minus 6 right parenthesis squared equals 13
  3. x squared plus open parentheses y minus 6 close parentheses squared equals 1
  4. x squared plus left parenthesis y minus 5 right parenthesis squared equals 13

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 General equation of a circle with center left parenthesis h comma k right parenthesis spaceand radius r is: left parenthesis x minus h right parenthesis squared plus left parenthesis y minus k right parenthesis squared equals r squared.

The correct answer is: x squared plus left parenthesis y minus 6 right parenthesis squared equals 13


    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 (0, 6) and the point on the circle (2, 3) is equal to radius
    Radius = square root of left parenthesis 2 minus 0 right parenthesis squared plus left parenthesis 3 minus 6 right parenthesis squared end root
    equals square root of 2 squared plus negative 3 squared end root
equals square root of 4 plus 9 end root
equals square root of 13
    Equation of a circle whose center 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 h right parenthesis squared plus left parenthesis y minus k right parenthesis squared equals left parenthesis square root of 13 right parenthesis squared space left curly bracket space h e r e space comma space h space equals space 0 space a n d space k space equals space 6 space right curly bracket
left parenthesis x minus 0 right parenthesis squared plus left parenthesis y minus 6 right parenthesis squared equals left parenthesis square root of 13 right parenthesis squared
left parenthesis x right parenthesis squared plus left parenthesis y minus 6 right parenthesis squared equals left parenthesis square root of 13 right parenthesis squared
x squared plus left parenthesis y minus 6 right parenthesis squared equals 13
    therefore space T h e space s t a n d a r d space e q u a t i o n space o f space t h e space c i r c l e space i s space x squared plus left parenthesis y minus 6 right parenthesis squared equals 13..

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