Question 769733
Find an equation for the ellipse satisfying the given conditions:
Ends of major axis (±6,0); passes through (2,3).
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Given 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 the center
center: (0,0)
a=6 (distance from center to vertices)
a^2=36
solving for b using coordinates of given point (2,3)
{{{x^2/36+y^2/b^2=1}}}
{{{2^2/36+3^2/b^2=1}}}
{{{4/36+9/b^2=1}}}
9/b^2=1-1/9=8/9
b^2/9=9/8
b^2=81/8
Equation:{{{x^2/36+8y^2/81=1}}}