Question 791154
Write an equation for the ellipse in standard form whose foci: (-3,4) and (7,4) passes through the point (2,1)
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Given foci data shows ellipse has a horizontal major axis.
Its standard form of equation: {{{(x-h)^2/a^2+(y-k)^2/b^2=1}}},a>b, (h,k)=(x,y) coordinates of center.
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center: (2,4)
plug in coordinates of center and given point(2,1)
{{{(2-2)^2/a^2+(4-1)^2/b^2=1}}}
{{{(0)^2/a^2+(3)^2/b^2=1}}}
0+9/b^2=1
b^2=9
b=√9=3
c=5(distance from center to foci
c^2=25
c^2=a^2-b^2
a^2=c^2+b^2=25+9=34
Equation of given ellipse:
{{{(x-2)^2/34+(y-4)^2/9=1}}}