What is 25x^2-9y^2+100x-54y+10=0 ?

The solution to 25x^2-9y^2+100x-54y+10=0 is Hyperbola with (h,k)=(-2,-3),a= 3/5 ,b=1

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25x^2-9y^2+100x-54y+10=0

25 x^{2} - 9 y^{2} + 100 x - 54 y + 10 = 0

(h, k) = (- 2, - 3), a = \frac{3}{5}, b = 1

Solution steps

25 x^{2} - 9 y^{2} + 100 x - 54 y + 10 = 0

Rewrite

25 x^{2} - 9 y^{2} + 100 x - 54 y + 10 = 0

in the form of a standard hyperbola equation

\frac{( x - ( - 2 ) ) ^{2}}{( \frac{3}{5} ) ^{2}} - \frac{( y - ( - 3 ) ) ^{2}}{1 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 2, - 3), a = \frac{3}{5}, b = 1

y^{2} = x^{2} + 8

9 x^{2} + 36 = y^{2} + 36 x + 6 y

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

25 y^{2} - 12 x^{2} - 48 x - 75 y = 0

\frac{( y + 1 ) ^{2}}{5 ^{2}} - \frac{( x - 1 ) ^{2}}{1 ^{2}} = 1

What is 25x^2-9y^2+100x-54y+10=0 ?
The solution to 25x^2-9y^2+100x-54y+10=0 is Hyperbola with (h,k)=(-2,-3),a= 3/5 ,b=1