((x-3)^2)/9-((y-6)^2/16)=1

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Solution for ((x-3)^2)/9-((y-6)^2/16)=1 equation: 


x in (-oo:+oo)

t_1 = -(((y-6)^2)/16)-1

((x-3)^2)/9+t_1 = 0

((x-3)^2)/9+(9*t_1)/9 = 0

(x-3)^2+9*t_1 = 0

9*t_1+x^2-6*x+9 = 0

(9*t_1+x^2-6*x+9)/9 = 0

(9*t_1+x^2-6*x+9)/9 = 0 // * 9

9*t_1+x^2-6*x+9 = 0

9*t_1+x^2-6*x+9 = 0

DELTA = (-6)^2-(1*4*(9*t_1+9))

DELTA = 36-4*(9*t_1+9)

36-4*(9*t_1+9) = 0

36-4*(9*t_1+9) = 0

-36*t_1 = 0

-36*t_1 = 0

-36*t_1 = 0 // : -36

t_1 = 0

DELTA = 0  <=>  t_4 = 0

x = 6/(1*2) i t_1 = 0

x = 3 i t_1 = 0

( x = ((36-4*(9*t_1+9))^(1/2)+6)/(1*2) or x = (6-(36-4*(9*t_1+9))^(1/2))/(1*2) ) i t_1 > 0

( x = ((36-4*(9*t_1+9))^(1/2)+6)/2 or x = (6-(36-4*(9*t_1+9))^(1/2))/2 ) i t_1 > 0

t_1+0 > 0

t_1 > 0

t_1+0 > 0 // - 0

t_1 > 0

x in { 3, ((36-4*(9*(-(((y-6)^2)/16)-1)+9))^(1/2)+6)/2, (6-(36-4*(9*(-(((y-6)^2)/16)-1)+9))^(1/2))/2 }

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