Question 824639
A hyperbola has center (0,0) and one vertex A(√6 , 0)
a) find the equation if fit passed through J(9,5)
b) find the value of x if K(x,2) is on the hyperbola
c) find the value of y if I(3,y) is on the hyperbola
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Hyperbola has a horizontal transverse axis with center at the origin.
Its standard form of equation: {{{x^2/a^2-y^2/b^2=1}}}
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a=√6
a^2=6
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a) solving for b^2:
{{{9^2/6-5^2/b^2=1}}}
{{{81/6-25/b^2=1}}} 
{{{25/b^2=81/6-1}}} 
{{{25/b^2=75/6}}}
b^2=(6)(25)/75=2
Equation:
{{{x^2/6-y^2/2=1}}}
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b){{{x^2/6-2^2/2=1}}}
{{{x^2/6-4/2=1}}}
x^2/6=3
x^2=18
x=±√18=±4.2426
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c){{{3^2/6-y^2/2=1}}}
{{{9/6-y^2/2=1}}}
y^2/2=9/6-1=3/6
y^2=1
y=±1