The equation x^2 + y^2 – 6x + 4y = 4 describes a circle. Which equation describes the same circle?A. (x – 3)^2 + (y + 2)^2 = 4B. (x – 3)^2 + (y + 2)^2 = 17C. (x – 3)^2 + (y – 2)^2 = 4D. (x – 3)^2 + (y – 2)^2 = 17

Answers 1

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.