0Find 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
