Question

The difference of the slopes of the lines of the 3 x square - 4 x square + y square is equals to zero is​

Answer 1

Answer:

Consider the given pair of equation.

3x

2

−4xy+y

2

=0

We know that the standard joint equation of two line is,

ax

2

+2hxy+by

2

=0

Therefore,

a=3

2h=−4

b=1

Let m

1

and m

2

be the slopes of both the lines. Then,

m

1

+m

2

=−

b

2h

m

1

+m

2

=−

1

(−4)

=4

And,

m

1

m

2

=

b

a

m

1

m

2

=

1

3

=3

We know that,

(m

1

−m

2

)

2

=(m

1

+m

2

)

2

−4m

1

m

2

(m

1

−m

2

)

2

=(4)

2

−4(3)

(m

1

−m

2

)

2

=16−12

(m

1

−m

2

)

2

=4

∣m

1

−m

2

∣=2

Hence, the difference of the slopes is 2.