Question 668323
find the equation of the ellipse with center (-2,3) major axis vertical; length of major axis is 4; and length of minor axis is 1
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Standard form of equation for an ellipse with vertical major axis: {{{(x-h)^2/b^2+(y-k)^2/a^2=1}}}, a>b, (h,k)=(x,y) coordinates of center.
For given problem:
given center: (-2,3)
given length of vertical major axis=4=2a
a=2
a^2=4
given length of minor axis=1=2b
b=1/2
b^2=1/4
Equation of given ellipse:
{{{(x+2)^2/(1/4)+(y-3)^2/4=1}}}
{{{4(x+2)^2+(y-3)^2/4=1}}}