Question 866623
{{{16x^2-196x+288-9y^2=0}}}
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{{{16x^2-196x-9y^2=-288}}}
{{{16(x^2-(49/4)x)-9y^2=-288}}}----This should be a hyperbola...
{{{16(x^2-(49/4)x+(49/8)^2)-9y^2=-288+16(49/8)^2}}}---Completing the Square
{{{16(x-49/8)^2-9y^2=-288+(4*4*7*7*7*7)/(2*4*2*4)}}}
{{{16(x-49/8)^2-9y^2=-288+49*49/4=(2401/4-288)}}}
{{{16(x-49/8)^2-9y^2=(2401-1152)/4}}}
{{{16(x-49/8)^2-9y^2=1249/4}}}
{{{(4/1249)16(x-49/8)^2-(4/1249)9y^2=1}}}
{{{(64/1249)(x-49/8)^2-(36/1249)y^2=1}}}
{{{highlight((x-49/8)^2/(1249/64)-y^2/(1249/36)=1)}}}
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Note that {{{a^2=1249/64}}} and {{{b^2=1249/36}}}.