What is 4x^2-4y^2+20x-16y+25=0 ?

The solution to 4x^2-4y^2+20x-16y+25=0 is Hyperbola with (h,k)=(-5/2 ,-2),a=2,b=2

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4x^2-4y^2+20x-16y+25=0

4 x^{2} - 4 y^{2} + 20 x - 16 y + 25 = 0

(h, k) = (- \frac{5}{2}, - 2), a = 2, b = 2

Solution steps

4 x^{2} - 4 y^{2} + 20 x - 16 y + 25 = 0

Rewrite

4 x^{2} - 4 y^{2} + 20 x - 16 y + 25 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (- \frac{5}{2}, - 2), a = 2, b = 2

\frac{( x ^{(2)} )}{( 25 )} - \frac{( y ^{(2)} )}{( 11 )} = 1

a^{2} - b^{2} - 4 a + 2 b = 19

y^{2} + 1 = x^{2} + 8 x

9 x^{2} - y^{2} = 1

5 x^{2} - 5 y^{2} + 20 x - 60 y = 185

What is 4x^2-4y^2+20x-16y+25=0 ?
The solution to 4x^2-4y^2+20x-16y+25=0 is Hyperbola with (h,k)=(-5/2 ,-2),a=2,b=2