Answer to Question #141909 in Analytic Geometry for Dhruv rawat

Question #141909
The equation x^2+y^2-2xy+2x++1=0 represents a parabola
1
Expert's answer
2020-11-02T18:43:25-0500

x2+y22xy+2x+1=0\\ x^{2}+y^{2}-2xy+2x+1=0 is the given equation.


The general equation of 2nd degree in two variables x,y is

ax2+by2+2hxy+2gx+2fy+c=0ax^{2}+by^{2}+2hxy+2gx+2fy+c=0


Comparing this with the given equation we get a=1,b=1,h=-1,g=1,f=0,c=1.


Δ=ahghbfgfc\Delta=\begin{vmatrix} a & h & g\\ h & b & f\\ g & f & c \end{vmatrix} =111110101\begin{vmatrix} 1 & -1 & 1 \\ -1 & 1 & 0\\ 1 & 0 & 1 \end{vmatrix} =1+1*(-1)+1*(-1)=-1\neq 0.


h2ab=11=0h^{2}-ab=1-1=0 .


Therefore it represents a parabola.


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment