What is 4y^2-x^2+2x+16y+7=0 ?

The solution to 4y^2-x^2+2x+16y+7=0 is Hyperbola with (h,k)=(1,-2),a=sqrt(2),b=2sqrt(2)

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4y^2-x^2+2x+16y+7=0

4 y^{2} - x^{2} + 2 x + 16 y + 7 = 0

(h, k) = (1, - 2), a = 2, b = 22

Solution steps

4 y^{2} - x^{2} + 2 x + 16 y + 7 = 0

Rewrite

4 y^{2} - x^{2} + 2 x + 16 y + 7 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (1, - 2), a = 2, b = 22

(x - 3) (x + 1) = yy

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

x^{2} + 6 x - 4 y^{2} - 8 y + 9 = 0

y^{2} = 3 6^{2} + x^{2}

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

What is 4y^2-x^2+2x+16y+7=0 ?
The solution to 4y^2-x^2+2x+16y+7=0 is Hyperbola with (h,k)=(1,-2),a=sqrt(2),b=2sqrt(2)