How do you find all the critical points to graph x2y210x10y1=0 including vertices, foci and asymptotes?

1 Answer
Oct 20, 2016

The vertices are (6,5) and (4,5)
The foci are (5+2,5 and (52,5)
The asymptotes are y=x10 and ygraph{x2y210x10y1=0[13.83,26.17,15.28,4.72]}=x

Explanation:

(x210x)(y2+10y)=1
Completing the squares (x5)2(y+5)5=1
(x5)21(y+5)21=1
So the certer is (5,5)
The vertices are (6,5) and (4,5)
The slope of the asymptotes are 1 and 1
The equations of the asymptotes are y=5+1(x5)=x10 and y=51(x5)=x
we need to calculate c=±1+1=2
c is the distance between the certer and the focus
And the foci are (5+2,5 and (52,5)