What is the center x^2-y^2+7x+8y=5 ?

The center x^2-y^2+7x+8y=5 is (-7/2 ,4)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

center x^2-y^2+7x+8y=5

center

x^{2} - y^{2} + 7 x + 8 y = 5

(- \frac{7}{2}, 4)

Solution steps

x^{2} - y^{2} + 7 x + 8 y = 5

Rewrite

x^{2} - y^{2} + 7 x + 8 y = 5

in the form of a standard hyperbola equation

\frac{( x - ( - \frac{7}{2} ) ) ^{2}}{( \frac{5}{2} ) ^{2}} - \frac{( y - 4 ) ^{2}}{( \frac{5}{2} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- \frac{7}{2}, 4), a = \frac{5}{2}, b = \frac{5}{2}

And the center is:

(- \frac{7}{2}, 4)

\frac{( x - 4 ) ^{2}}{36} - \frac{( y - 2 ) ^{2}}{9} = 1

9 y^{2} - 49 x^{2} = 441

4 x^{2} - 9 y^{2} + 32 x + 36 y + 64 = 0

4 x^{2} - 45 y^{2} = 180

\frac{( y - 2 ) ^{2}}{9} - \frac{( x - 1 ) ^{2}}{16} = 1