Question 968831


the standard form equation of an ellipse is

a. if the major axis of this ellipse is horizontal:

{{{x^2/a^2+y^2/b^2=1}}} where  {{{a>b}}} 

b. if the major axis of this ellipse is vertical:

{{{x^2/b^2+y^2/a^2=1}}}  {{{a>b}}}

the standard form equation  for the translation({{{h}}},{{{k}}}) of an ellipse is:

{{{(x-h)^2/a^2+(y-k)^2/b^2=1}}}

you are given {{{4x^2+y^2-2y=15}}}

so, complete squares

 {{{4x^2+(y^2-2y+_)-_=15}}} 

 {{{4x^2/4+(y^2-2y+1^2)/4-1^2/4=15/4}}}

 {{{x^2+(1/4)(y^2-2y+1)-1/4=15/4}}}

{{{(x-0)^2+(1/4)(y-1)^2=15/4+1/4}}}

{{{(x-0)^2+(1/4)(y-1)^2=16/4}}}

{{{(x-0)^2+(1/4)(y-1)^2=4}}}.........both sides divide by {{{4}}}

{{{(x-0)^2/4+(1/4)(y-1)^2/4=4/4}}}

{{{highlight((x-0)^2/4+(1/16)(y-1)^2=1)}}}