Question 1159590


Determine whether the major axis is on the x  -  or y-axis.
If the given coordinates of the vertices and foci have the form (±{{{a}}},{{{0}}}) and (±{{{c}}},{{{0}}}) respectively, then the major axis is parallel to the x-axis. Use the standard form: 

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

If the given coordinates of the vertices and foci have the form ({{{0}}},±{{{a}}}) and ({{{0}}},±{{{c}}}) respectively, then the major axis is parallel to the x-axis. Use the standard form: 

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


given:
a vertex at ({{{1}}},{{{9}}})=>   is the form ({{{0}}},±{{{a}}})

so, go with

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


if the center is at ({{{1}}},{{{4}}})=>{{{h=1}}} and {{{k=4}}}


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


if the length of minor axis is  {{{6}}}=>{{{2a=6}}}=>{{{a=3}}}


{{{(x-1)^2/3^2+(y-4)^2/a^2=1}}}


({{{1}}},{{{9}}})=>use to find {{{a}}}

{{{(1-1)^2/9+(9-4)^2/b^2=1}}}

{{{0/9+25/a^2=1}}}

{{{25=a^2}}}

your equation is:

{{{(x-1)^2/9+(y-4)^2/25=1}}}


{{{drawing( 600, 600, -10, 10, -10, 10,
circle(1,4,.12), locate(1,4,C(1,4)),
circle(1,9,.12), locate(1,9,V(1,9)),
 graph( 600, 600, -10, 10, -10, 10,-sqrt(25(1-(x-1)^2/9))+4 ,sqrt(25(1-(x-1)^2/9))+4)) }}}