Convert the equation to the standard form for a hyperbola by completing the square on x and y. x2 - y2 + 6x

Science & Mathematics by Anonymous 2018-05-25 11:05:38

Social Science

Convert the equation to the standard form for a hyperbola by completing the square on x and y. x2 - y2 + 6x - 4y + 4 = 0?

5 answers

Anonymous

x^2-y^2+6x-4y+4=0 x^2+6x -y^2-4y +4 = 0 x^2+6x+9-9 - y^2+4y+4 -4 + 4 = 0 (x^2+6x+9) -9 - (y^2+4y+4) +4 +4 = 0 (x+3)^2 -(y+2)^2 = 1 Hyperbola with center (-3,-2) and transverse axis x axis
Anonymous

x² - y² + 6x - 4y + 4 = 0 x² + 6x - y² - 4y = - 4 x² + 6x + 9 - y² - 4y = - 4 + 9 x² + 6x + 9 - y² - 4y - 4 = - 4 + 9 - 4 (x² + 6x + 9) - (y² + 4y + 4) = 1 (x + 3)² - (y + 2)² = 1
Anonymous

x²+6x-(y²+4y)+4=0 Complete the square x²+6x+9-9-(y²+4y+4-4)+4=0 (x+3)²-9-(y+2)²+4+4=0 (x+3)²-(y+2)²=1 Check it http://www.wolframalpha.com/input/?i=x2+... OK!
Anonymous

No
Anonymous

( x + 3 )² - ( y + 2 )² = - 4 + 9 + 4 = 9===> ( x + 3 )² / 9 - ( y + 2 )² / 9 = 1