What is -4x^2+5y^2+8x-30y+21=0 ?

The solution to -4x^2+5y^2+8x-30y+21=0 is Hyperbola with (h,k)=(1,3),a=2,b=sqrt(5)

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-4x^2+5y^2+8x-30y+21=0

- 4 x^{2} + 5 y^{2} + 8 x - 30 y + 21 = 0

(h, k) = (1, 3), a = 2, b = 5

Solution steps

- 4 x^{2} + 5 y^{2} + 8 x - 30 y + 21 = 0

Rewrite

- 4 x^{2} + 5 y^{2} + 8 x - 30 y + 21 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (1, 3), a = 2, b = 5

\frac{( x + 4 ) ^{2}}{4} - \frac{( y - 1 ) ^{2}}{9} = 1

16 x^{2} - 96 x - 25 y^{2} + 200 y - 656 = 0

y^{2} = x^{2} + 17

y^{2} = x^{2} + 13

y^{2} = x^{2} + 14

What is -4x^2+5y^2+8x-30y+21=0 ?
The solution to -4x^2+5y^2+8x-30y+21=0 is Hyperbola with (h,k)=(1,3),a=2,b=sqrt(5)