Question 818442
An ellipse has center ( 0,0) and one vertex a(10,0) . Find the equation of the ellipse if it passes through r(6,4).
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Given ellipse has a horizontal major axis and center at the origin.
Its standard form of equation: {{{x^2/a^2+y^2/b^2=1}}}, a>b
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a=10(distance from center to vertices)
a^2=100
equation:{{{6^2/100+4^2/b^2=1}}}
solving for b^2
{{{36/100+16/b^2=1}}}
{{{16/b^2=1-(36/100)}}}
{{{16/b^2=64/100)}}}
{{{b^2=100*16/64=25}}}
equation of given ellipse:{{{x^2/100+y^2/25=1}}}