What is -4x^2+7y^2+8x+42y+31=0 ?

The solution to -4x^2+7y^2+8x+42y+31=0 is Hyperbola with (h,k)=(1,-3),a=2,b=sqrt(7)

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-4x^2+7y^2+8x+42y+31=0

- 4 x^{2} + 7 y^{2} + 8 x + 42 y + 31 = 0

(h, k) = (1, - 3), a = 2, b = 7

Solution steps

- 4 x^{2} + 7 y^{2} + 8 x + 42 y + 31 = 0

Rewrite

- 4 x^{2} + 7 y^{2} + 8 x + 42 y + 31 = 0

in the form of a standard hyperbola equation

\frac{( y - ( - 3 ) ) ^{2}}{2 ^{2}} - \frac{( x - 1 ) ^{2}}{( 7 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (1, - 3), a = 2, b = 7

4 x^{2} - 4 y^{2} - 4 x + 8 y - 19 = 0

25 x^{2} - 16 y^{2} = 400

9 x^{2} - 36 y^{2} = 324

\frac{( x - h ) ^{2}}{a ^{2}} - \frac{( y - k ) ^{2}}{b ^{2}} = 1

64 y^{2} - 36 x^{2} = 2304

What is -4x^2+7y^2+8x+42y+31=0 ?
The solution to -4x^2+7y^2+8x+42y+31=0 is Hyperbola with (h,k)=(1,-3),a=2,b=sqrt(7)