Question 632168
a conic section is described by x^2+6x+5/8y^2=-4. what type of conic section does this repersent?
x^2+6x+5/8y^2=-4.
complete the square for the x-term
(x^2+6x+9)+5y^2/8=-4+9
(x+3)^2+5y^2=5
divide by 5
{{{(x+3)^2/5+y^2/1=1}}}
This is an equation of an ellipse with  horizontal major axis
Its standard form: {{{(x-h)^2/a^2+(y-k)^2/b^2=1}}} a>b, (h,k)=(x,y) coordinates of center