Question 814449
Graph each ellipse by hand. Give the domain and range. Identify the center. Do not use a calculator.
(x + 3)2 over 16 + (y - 2)2 over 36 = 1
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{{{((x+3)^2/16)+(y-2)^2/36=1)}}}
Standard form of equation for an ellipse with vertical major axis:
{{{((x+h)^2/b^2)+(y-k)^2/a^2=1)}}}
 
a^2=36
a=√36=6
b^2=16
b=√16=4
..
center: (-3,2)
domain: (-7,1)
range: (-4,8)
..
see graph below:
{{{y=(36-(9/4)*(x+3)^2)^.5+2}}}

 {{{ graph( 300, 300, -10, 10, -10, 10,(36-(9/4)*(x+3)^2)^.5+2,-(36-(9/4)*(x+3)^2)^.5+2) }}}