What is (x^2)/(a^2)-(y^2)/(a-16)=1 ?

The solution to (x^2)/(a^2)-(y^2)/(a-16)=1 is Hyperbola with (h,k)=(0,0),a=a,b=sqrt(a-16)

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(x^2)/(a^2)-(y^2)/(a-16)=1

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

(h, k) = (0, 0), a = a, b = a - 16

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

\frac{( x - 0 ) ^{2}}{a ^{2}} - \frac{( y - 0 ) ^{2}}{( a - 16 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, 0), a = a, b = a - 16

5 y^{2} - 6 x - 3 x^{2} - 10 y - 13 = 0

[f (x)]^{2} = 5 x^{2} - x + 3

2 y^{2} + \frac{10}{2} x^{2} - 8 + 1 = 3 y^{2} - 4

3 x^{2} - 4 y^{2} = 36

13 x^{2} - 14 x - 26 = 13 y^{2} + 18 y - 7

What is (x^2)/(a^2)-(y^2)/(a-16)=1 ?
The solution to (x^2)/(a^2)-(y^2)/(a-16)=1 is Hyperbola with (h,k)=(0,0),a=a,b=sqrt(a-16)