Question

The combined equation of the lines passing through the origin and having slopes 3 and - 2 is
6x'- xy + y =0
x + xy-6y' =0
6x + xy - y =0
x - xy +6y' =0​

Answer 1

Answer:

Hi Mate

Given homogeneous equation is 5x

2

+2xy−3y

2

=0 which is factorisable as

5x

2

+5xy−3xy−3y

2

=0

⇒5x(x+y)−3y(x+y)=0

⇒(x+y)(5x−3y)=0

x+y=0 and 5x−3y=0 are the two lines represented by the given equation.

⇒Their slopes are –1 and

3

5

.

Required two lines are respectively perpendicular to these lines.

∴ Slopes of required lines are 1 and −

5

3

and the lines pass through origin.

∴ Their individual equations are y=1⋅x and y=−

5

3

x

i.e.,x−y=0,3x+5y=0

∴ Their joint equation is (x−y)(3x+5y)=0

⇒3x

2

−3xy+5xy−5y

2

=0

⇒3x

2

+2xy−5y

2

=0

Hence 3x

2

+2xy−5y

2

=0 is the required joint equation.

Hope it helps you

Have a great day!!

Answer 2

Step-by-step explanation:

6x'- xy + y =0

x + xy-6y' =0

6x + xy - y =0

x - xy +6y' =0