Question

College precalc:1) determine the important values and sketch a graph of the equation x^2-y^2=10(x-y)+1

Answer 1

We are given the equation

`x^2-y^2=10(x-y)+1`

Note: Hyperbola Formula

We will simpify this

`\begin{gathered} x^2-y^2=10(x-y)+1 \\ x^2-y^2=10x-10y+1 \\ x^2-10x-y^2+10y=1 \\ x^2-10x+25-25-y^2+10y=1 \\ x^2-10x+25-y^2+10y-25=1 \\ x^2-10x+25-(y^2-10y+25)=1 \\ (x-5)^2-(y-5)^2=1 \\ \\ ((x-5)^2)/(1)-((y-5)^2)/(1)=1 \end{gathered}`

Thus, we draw the hyperbola

`((x-5)^2)/(1)-((y-5)^2)/(1)=1`