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Equation of circle

B.Sudhakar
07/02/2017 0 0

Find the equation of a circle with centre C ( 2 , 4 ) and the circle passes through point P ( 5 , 8 ).

First let us find the radius of the circle ie: length of line segment C P using distance formula.

Length C P = radius of the circle = √ ( 5 - 2 )² +( 8 - 4 )² = √ 9 + 16 = √ 25 = 5

Equation of circle with centre ( h , k ) = ( x - h )² + ( y - k )² = r²

h = 2 , k = 4 and r = 5 by substituting all these values 

( x - 2 )² + ( y - 4 )² = 5²

= ( x² + 4 - 4 x ) + ( y² + 16 - 8y ) = 25

= x² + y² - 4 x - 8 y + 20 - 25 = 0

= x² + y² - 4 x - 8 y - 5 =0

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