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

The solution to 3x^2-5y^2+6x+10=32 is Hyperbola with (h,k)=(-1,0),a= 5/(sqrt(3)),b=sqrt(5)

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

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

(h, k) = (- 1, 0), a = \frac{5}{3}, b = 5

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

\frac{( x - ( - 1 ) ) ^{2}}{( \frac{5}{3} ) ^{2}} - \frac{( y - 0 ) ^{2}}{( 5 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 1, 0), a = \frac{5}{3}, b = 5

8 y^{2} - 2 x^{2} = 16

y^{2} = 100 + x^{2}

x^{(2)} - 2 x - 4 y^{(2)} + 24 y = 31

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

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

What is 3x^2-5y^2+6x+10=32 ?
The solution to 3x^2-5y^2+6x+10=32 is Hyperbola with (h,k)=(-1,0),a= 5/(sqrt(3)),b=sqrt(5)