SOLUTION: Find the value(s) of k such that the graph of the equation k(x^2+y^2 )+x^2-y^2+x+y=0 is a parabola an ellipse a hyperbola a pair of intersecting lines

Algebra ->  Trigonometry-basics -> SOLUTION: Find the value(s) of k such that the graph of the equation k(x^2+y^2 )+x^2-y^2+x+y=0 is a parabola an ellipse a hyperbola a pair of intersecting lines       Log On


   

Question 1195159: Find the value(s) of k such that the graph of the equation k(x^2+y^2 )+x^2-y^2+x+y=0 is
a parabola
an ellipse
a hyperbola
a pair of intersecting lines
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
k(x^2+y^2 )+x^2-y^2+x+y=0
kx^2+ky^2+x^2-y^2+x+y=0
(k+1)x^2+(k-1)y^2+x+y=0
Check the expression
-4%28k%2B1%29%28k-1%29
-
-4%28k%5E2-1%29, and work with that. You can find reference information in your book in some online sources.
https://www.brainkart.com/article/Conic-Sections_39168/
https://www.varsitytutors.com/hotmath/hotmath_help/topics/conic-sections-and-standard-forms-of-equations
http://mathcentral.uregina.ca/QQ/database/QQ.09.06/h/robin2.html


For intersecting lines,
k%2B1=-%28k-1%29
k%2B1=-k%2B1
2k=0
highlight_green%28k=0%29