What is ((y-1/4)^2)/4-((x+3)^2)/9 =1 ?

The solution to ((y-1/4)^2)/4-((x+3)^2)/9 =1 is Hyperbola with (h,k)=(-3, 1/4),a=2,b=3

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((y-1/4)^2)/4-((x+3)^2)/9 =1

\frac{( y - \frac{1}{4} ) ^{2}}{4} - \frac{( x + 3 ) ^{2}}{9} = 1

(h, k) = (- 3, \frac{1}{4}), a = 2, b = 3

Solution steps

\frac{( y - \frac{1}{4} ) ^{2}}{4} - \frac{( x + 3 ) ^{2}}{9} = 1

Rewrite

\frac{( y - \frac{1}{4} ) ^{2}}{4} - \frac{( x + 3 ) ^{2}}{9} = 1

in the form of a standard hyperbola equation

\frac{( y - \frac{1}{4} ) ^{2}}{2 ^{2}} - \frac{( x - ( - 3 ) ) ^{2}}{3 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 3, \frac{1}{4}), a = 2, b = 3

f (x) f (x) = \frac{15 x ^{3} - 3 x ^{2} - 12 x}{3 x}

\frac{y ^{2}}{100} - \frac{x ^{2}}{49} = 1

\frac{x ^{2}}{16} - \frac{y ^{2}}{33} = 1

6 x^{2} - 5 y^{2} + 12 x - 30 y - 9 = 0

18 y^{2} - 4 x^{2} = 1

What is ((y-1/4)^2)/4-((x+3)^2)/9 =1 ?
The solution to ((y-1/4)^2)/4-((x+3)^2)/9 =1 is Hyperbola with (h,k)=(-3, 1/4),a=2,b=3