remember completeing square? do tat for x's and y's
so
(2x²-16x)+(-4y²+48y)-120=0 2(x²-8x)-4(y²-12y)-120=0 2(x²-8x+16-16)-4(y²-12y+36-36)-120=0 2((x-4)²-16)-4((y-6)²-36)-120=0 2(x-4)²-32-4(y-6)²+144-120=0 2(x-4)²-4(y-6)²=8 divide both sides by 8 [tex] \frac{(x-4)^2}{4}- \frac{(y-6)^2}{2}=1 [/tex] das be hyperbola
2. (2x²+20x)+(4y²+8y)+46=0 2(x²+10x)+4(y²+2y)+46=0 2(x²+10x+25-25)+4(y²+2y+1-1)+46=0 2((x+5)²-25)+4((y+1)²-1)+46=0 2(x+5)²-50+4(y+1)²-4+46=0 2(x+5)²+4(y+1)²-8=0 2(x+5)²+4(y+1)²=8 divide by 8 [tex] \frac{(x+5)^2}{4}+ \frac{(y+1)^2}{2} =1[/tex] das is elipse (becase it is plus)
