Question

Sa se aduca la forma canonica forma 3x^{2} +8xy+3y^{2} -4x+2y-3=0 . Va rog sa ma ajutati

Answer 1

Răspuns:

3x2−8xy−3y2=0

⇒3x2−9xy+xy−3y2=0

⇒3x(x−3y)+y(x−3y)=0

⇒(3x+y)(x−3y)=0

linile sunt 3x+y=0 si x−3y=0





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Class 7

>>Maths

>>The Triangle and Its Properties

>>Isosceles and Equilateral Triangles

>>Prove that the lines represented by 3x^2

Question



Prove that the lines represented by 3x2−8xy−3y2=0 and x+2y=3 form the sides of an isosceles right angled triangle.

Medium

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Solution



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3x2−8xy−3y2=0

⇒3x2−9xy+xy−3y2=0

⇒3x(x−3y)+y(x−3y)=0

⇒(3x+y)(x−3y)=0

Lines are 3x+y=0 and x−3y=0

(Refer to Image)  

verticalele sunt  (0,0)

x+2y=3                 y=−3x

x−3y=0                  x+2(−3x)=3

x=3y                      −5x=3

3x+2y=3               x=−3/5,y=−3(−3/5)=9/5

5y=3

y=3/5   x=3(3/5)