What is x^2-y^2-x+y-(-10)=0 ?

The solution to x^2-y^2-x+y-(-10)=0 is Hyperbola with (h,k)=(1/2 , 1/2),a=sqrt(10),b=sqrt(10)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

x^2-y^2-x+y-(-10)=0

x^{2} - y^{2} - x + y - (- 10) = 0

(h, k) = (\frac{1}{2}, \frac{1}{2}), a = 10, b = 10

Solution steps

x^{2} - y^{2} - x + y - (- 10) = 0

Rewrite

x^{2} - y^{2} - x + y - (- 10) = 0

in the form of a standard hyperbola equation

\frac{( y - \frac{1}{2} ) ^{2}}{( 10 ) ^{2}} - \frac{( x - \frac{1}{2} ) ^{2}}{( 10 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (\frac{1}{2}, \frac{1}{2}), a = 10, b = 10

y^{2} = (\frac{6}{5})^{2} + (2 - x)^{2}

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

y (y + 2) = x^{2}

x^{2} + 1 x + y^{2} - 2 y^{2} = 25

10 y^{2} - 25 x^{2} = 400

What is x^2-y^2-x+y-(-10)=0 ?
The solution to x^2-y^2-x+y-(-10)=0 is Hyperbola with (h,k)=(1/2 , 1/2),a=sqrt(10),b=sqrt(10)