Question 682050
{{{9(x+4)^2+(y+7)^2=81}}}

{{{9(x+4)^2/81+(y+7)^2/81=81/81}}}

{{{(x+4)^2/9+(y+7)^2/81=1}}}

{{{(x+4)^2/3^2+(y+7)^2/9^2=1}}}


{{{b=3}}}, {{{a=9}}}, {{{h=-4}}}, and {{{k=-7}}}


Center: ({{{h}}}, {{{k}}})=({{{-4}}}, {{{-7}}})

Vertices: (-4, -7 ± 9)  or

        ({{{-4}}},{{{2}}}), ({{{-4}}},{{{-16}}})

Co-vertices: (-4 ± 3, -7) or ({{{-1}}},{{{-7}}}), and ({{{-7}}},{{{-7}}})

Length of Major Axis: {{{2a=18}}}

Length of Minor Axis: {{{2b=6}}}



{{{drawing(600,600,-10, 10, -20,10,grid(1),circle(-4,-7,0.2),circle(-1,-7,0.2),circle(-7,-7,0.2),
circle(-4,2,0.2),circle(-4,-16,0.2),graph(600,600,-10,10,-20,10,3*sqrt(-7-8x-x^2)-7,-3*sqrt(-7-8x-x^2)-7))}}}


2.

{{{(x-3)^2/9 + (y+3)^2/16 = 1}}}

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


{{{b=3}}}, {{{a=4}}}, {{{h=3}}}, and {{{k=-3}}}


Center: ({{{h}}}, {{{k}}})=({{{3}}}, {{{-3}}})

Vertices: (3, -3 ± 4)  or

        ({{{3}}},{{{1}}}), ({{{3}}},{{{-7}}})

Co-vertices: (3 ± 3, -3) or ({{{6}}},{{{-3}}}), and ({{{0}}},{{{-3}}})

Length of Major Axis: {{{2a=8}}}

Length of Minor Axis: {{{2b=6}}}





{{{drawing(600,600,-10, 10, -10,10,grid(1),circle(3,-3,0.2),circle(3,1,0.2),circle(3,-7,0.2),
circle(0,-3,0.2),circle(6,-3,0.2),graph(600,600,-10,10,-10,10,(1/3)*(4(sqrt(6x-x^2))-9),(1/3)*(-4(sqrt(6x-x^2))-9)))}}}