What is -3x^2+2y^2+18x-20y+17=0 ?

The solution to -3x^2+2y^2+18x-20y+17=0 is Hyperbola with (h,k)=(3,5),a=sqrt(3),b=sqrt(2)

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-3x^2+2y^2+18x-20y+17=0

- 3 x^{2} + 2 y^{2} + 18 x - 20 y + 17 = 0

(h, k) = (3, 5), a = 3, b = 2

Solution steps

- 3 x^{2} + 2 y^{2} + 18 x - 20 y + 17 = 0

Rewrite

- 3 x^{2} + 2 y^{2} + 18 x - 20 y + 17 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (3, 5), a = 3, b = 2

\frac{x ^{2}}{8 ^{2}} - \frac{y ^{2}}{5 ^{2}} = 1

4 y^{2} - x^{2} + 16 y + 12 = 0

3 x^{2} - 3 y^{2} + x + y + 1 = 0

- 4 x^{2} + y^{2} - 40 x - 16 = 0

x^{2} + 8 x - y^{2} - 4 y = 5

What is -3x^2+2y^2+18x-20y+17=0 ?
The solution to -3x^2+2y^2+18x-20y+17=0 is Hyperbola with (h,k)=(3,5),a=sqrt(3),b=sqrt(2)