Question 711592
Please put in standard form. (ellipse)
18x^2+9y^2=153-24x+6y
rearrange terms:
18x^2+24x+9y^2-6y=153
complete the square:
18(x^2+24x/18+9(y^2-6y/9=153
18(x^2+4x/3+9(y^2-2y/3=153
18(x^2+4x/3+16/36)+9(y^2-2y/3+4/36)=153+8+1
18(x+4/9)^2+9(y-1/9)^2=162
{{{(x+4/9)^2/9+(y-1/9)^2/18=1}}}
This is an equation of an ellipse with vertical major axis and center at (-4/9,1/9)
Its standard form: {{{(x-h)^2/b^2+(y-k)^2/a^2=1}}}, a>b, (h,k)=(x,y) coordinates of center