 Questions & Answers    Question Answers

# What are represented by the equation ${x^3} + {y^3} - xy(x + y) + {a^2}(y - x) = 0$  Answer Verified

Solution: -

First of all expand the equation and factories to solve them.

${x^3} + {y^3} - {x^2}y - x{y^2} + {a^2}(y - x) = 0$

Now take ${x^2}$ and ${y^2}$ common we get,

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

Now we take (y - x) as common we get,

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

By above equation we can say

y - x = 0....(1) and

$({y^2} - {x^2} + {a^2}) = 0....(2)$

Now equation (1) is the equation of straight line it is in the form of y = mx + c where c = 0 and the second equation is rectangular hyperbola,we can write the equation (2) as ${x^2} - {y^2} = {a^2}$.

Note: - For finding the nature of the equation. First of all break the equation into its simplest form. By breaking into the simplest form we can find the nature of the equation by comparing  with the equation we know.

Bookmark added to your notes.
View Notes
What are the Domains of the Earth  What are the Challenges of Democracy?  What are the Factorsof 17?  What are the Functions of the Human Skeletal System?  What are the Successor and Predecessor?  Factorisation  What is Mathematics?  What are The Fundamental Forces in Nature?  CBSE Class 11 Maths Formulas  Factorisation Using Division  