Question 1206909

5. a. Find the center and the radius of each circle

{{{(x - 3)^2 + (y + 5)^2 = 49}}}

compare to formula for circle

 {{{(x - h)^2 + (y -k)^2 = r^2}}} where {{{h}}},{{{k}}} are coordinates of center, {{{r }}}is radius


so, {{{h=3}}}, {{{k=-5}}}, and center is at ({{{3}}},{{{-5}}})

radius {{{r=sqrt(49)=7}}}



b. For each ellipse, determine the coordinates of the center, lengths of the major and minor axes.


{{{(x-4)^2/25 + (y+ 6)^2/49 = 1}}}

compare to formula for vertical ellipse

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

{{{h=4}}}

{{{k=-6}}}

center at ({{{4}}},{{{-6}}})

the major axes length {{{2a=2*sqrt(49)=2*7 =14}}}

and minor axes length {{{2b=2*sqrt(25)=2* 5=10}}}