What is 3y^2-5x^2+18y-40x-533=0 ?

The solution to 3y^2-5x^2+18y-40x-533=0 is Hyperbola with (h,k)=(-4,-3),a=4sqrt(10),b=4sqrt(6)

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3y^2-5x^2+18y-40x-533=0

3 y^{2} - 5 x^{2} + 18 y - 40 x - 533 = 0

(h, k) = (- 4, - 3), a = 410, b = 46

Solution steps

3 y^{2} - 5 x^{2} + 18 y - 40 x - 533 = 0

Rewrite

3 y^{2} - 5 x^{2} + 18 y - 40 x - 533 = 0

in the form of a standard hyperbola equation

\frac{( y - ( - 3 ) ) ^{2}}{( 4 10 ) ^{2}} - \frac{( x - ( - 4 ) ) ^{2}}{( 4 6 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 4, - 3), a = 410, b = 46

\frac{( y - 3 ) ^{2}}{9} - \frac{( x + 1 ) ^{2}}{27} = 1

y^{2} - 4 x^{2} - 2 y + 24 x = 51

\frac{( x - 1 ) ^{2}}{36} - \frac{( y + 2 ) ^{2}}{25} = 1

\frac{x ^{2}}{3 0 ^{2}} - \frac{y ^{2}}{4 4 ^{2}} = 1

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

What is 3y^2-5x^2+18y-40x-533=0 ?
The solution to 3y^2-5x^2+18y-40x-533=0 is Hyperbola with (h,k)=(-4,-3),a=4sqrt(10),b=4sqrt(6)