What is 4x^2-4y^2+28x-8y+53=0 ?

The solution to 4x^2-4y^2+28x-8y+53=0 is Hyperbola with (h,k)=(-7/2 ,-1),a=sqrt(2),b=sqrt(2)

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4x^2-4y^2+28x-8y+53=0

4 x^{2} - 4 y^{2} + 28 x - 8 y + 53 = 0

(h, k) = (- \frac{7}{2}, - 1), a = 2, b = 2

Solution steps

4 x^{2} - 4 y^{2} + 28 x - 8 y + 53 = 0

Rewrite

4 x^{2} - 4 y^{2} + 28 x - 8 y + 53 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (- \frac{7}{2}, - 1), a = 2, b = 2

\frac{( x - 2 ) ^{2}}{4} - \frac{( y + 3 ) ^{2}}{9} = 1

9 x^{2} - 4 y^{2} - 72 x + 16 y + 92 = 0

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

3 x^{2} - 3 y^{2} - 6 x = 0

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

What is 4x^2-4y^2+28x-8y+53=0 ?
The solution to 4x^2-4y^2+28x-8y+53=0 is Hyperbola with (h,k)=(-7/2 ,-1),a=sqrt(2),b=sqrt(2)