What is 3x^2-5y^2+6x+10y=32 ?

The solution to 3x^2-5y^2+6x+10y=32 is Hyperbola with (h,k)=(-1,1),a=sqrt(10),b=sqrt(6)

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3x^2-5y^2+6x+10y=32

3 x^{2} - 5 y^{2} + 6 x + 10 y = 32

(h, k) = (- 1, 1), a = 10, b = 6

Solution steps

3 x^{2} - 5 y^{2} + 6 x + 10 y = 32

Rewrite

3 x^{2} - 5 y^{2} + 6 x + 10 y = 32

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (- 1, 1), a = 10, b = 6

a^{2} - b^{2} = 12

\frac{( x - 3 ) ^{2}}{36} - \frac{( y - 4 ) ^{2}}{81} = 1

x^{2} - 2 x - y^{2} + 4 y = 7

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

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

What is 3x^2-5y^2+6x+10y=32 ?
The solution to 3x^2-5y^2+6x+10y=32 is Hyperbola with (h,k)=(-1,1),a=sqrt(10),b=sqrt(6)