Given
x² + y² - 6x + 4y = 4 describes a equation of circle
We are asked to find the standard form of equation of the circle
x² + y² - 6x + 4y = 4
Now we have find it completing square method
First separte x terms
( x² - 6x ) + ( y² + 4y ) = 4
The equation can be written as
[ x² - 2( x )( 3 ) ] + [ y² + 2( y )( 2 ) ] = 4
Adding subtracting 3², 2²
[ x² - 2( x )( 3 ) + 3² - 9 ] + [ y² + 2( y) (2) + 2² - 4 ] = 4
Using algebraic identities ( a + b)² = a² + b² + 2ab and (a - b)² = a² + b² - 2ab
( x - 3 )² + ( y + 2 )² - 13 = 4
( x - 3 )² + ( y + 2 )² = 4 + 13
( x - 3 )² + ( y + 2 )² = 17
Hence (B) ( x - 3 )² + ( y + 2 )² = 17 is the equation which describes the same circle.