Question 727427
1.  The standard form equation of an ellipse with a horizontal major axis with center at 
*[tex \LARGE (h,k)], vertices at *[tex \LARGE (\pm{a}\,+\,h,\,k)], and co-vertices at 
*[tex \LARGE (h,\,\pm{b}\,+\,k] is:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{(x\ -\ h)^2}{a^2}\ +\ \frac{(y\ -\ k)^2}{b^2}\ =\ 1] where *[tex \LARGE a\ >\ b]

given: vertex at ({{{-5}}},{{{0}}}) and co-vertex at ({{{0}}}, {{{4}}})

 
vertex ({{{a+h}}},{{{k}}}) ; so {{{a+h=-5}}} and {{{k=0}}}

co-vertex ({{{h}}},{{{b+k}}}) ; so {{{h=0}}} and {{{b+k=4}}}

if {{{h=0}}} than {{{a+0=-5}}}...=>..{{{a=-5}}} and {{{-a=5}}}

if {{{k=0}}}, than {{{b+0=4}}}.......or {{{b=4}}} and {{{-b=-4}}}

so, your equation is:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{(x\ -\ 0)^2}{5^2}\ +\ \frac{(y\ -\ 0)^2}{4^2}\ =\ 1] 


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{x^2}{25}\ +\ \frac{y^2}{16}\ =\ 1] 


{{{graph( 400, 400, -10, 10, -10, 10,x^2/25 +y^2/16 <= 1 )}}}