What is 4x^2-y^2+24x+40=0 ?

The solution to 4x^2-y^2+24x+40=0 is Hyperbola with (h,k)=(-3,0),a=2,b=1

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4x^2-y^2+24x+40=0

4 x^{2} - y^{2} + 24 x + 40 = 0

(h, k) = (- 3, 0), a = 2, b = 1

Solution steps

4 x^{2} - y^{2} + 24 x + 40 = 0

Rewrite

4 x^{2} - y^{2} + 24 x + 40 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (- 3, 0), a = 2, b = 1

4 x^{2} - y^{2} + 16 x + 2 y = 21

9 x^{2} - 4 y^{2} + 36 x + 40 y - 208 = 0

x^{2} - 5 y^{2} + 10 y + 4 x - 37 = 0

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

a^{2} - b^{2} = 14

What is 4x^2-y^2+24x+40=0 ?
The solution to 4x^2-y^2+24x+40=0 is Hyperbola with (h,k)=(-3,0),a=2,b=1