Question 734557
center at (6,5); focus at (11,5); ellipse passes through the point (6,8)
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Give data shows that ellipse has a horizontal major axis.
Its standard form of equation:{{{(x-h)^2/a^2+(y-k)^2/b^2=1}}}, (h,k)=(x,y) coordinates of center.
For given problem:
{{{(x-6)^2/a^2+(y-5)^2/b^2=1}}}
plug in given point(6,8)on the ellipse
{{{(6-6)^2/a^2+(8-5)^2/b^2=1}}}
{{{0+(3)^2/b^2=1}}}
{{{9=b^2}}}
{{{b=3}}}
c=5 (distance from center to focus (6 to 11))
c^2=25=a^2-b^2
a^2=c^2+b^2=25+9=34
Equation of given ellipse:
{{{(x-6)^2/34+(y-5)^2/9=1}}}