Question

If one of the lines given by, kx
2
+4xy−y
2
=0

is x + 2y = 0 , then find k​

Answer 1

Answer:

the answer is

Step-by-step explanation:

Find the value of k, if slope of one of the lines given by kx

2

+4xy−y

2

=0 exceeds the slope of the other by 8.

According to the problem:-

consider the given joint equation =kx

2

+4xy−y

2

comparing with ax

2

+2hxy+by

2

=0

We get,

a=k,2h=4,b=−1

Let the slopes of the two lines represented by given joint equation is m

1

andm

2

⇒ (m

1

+m

2

)=

b

−2h

=

−1

−4

⇒ m

1

+m

2

=4

and

m

1

.m

2

=d

b

a

=

−1

k

=−k

Given that ,

∣m

1

−m

2

∣=8

squaring both side

(m

1

−m

2

)

2

=64

since (m

1

+m

2

)

2

−4m

1

⋅m

2

=64

⇒ 4

2

−4(−k)=64

⇒ 4k=48

⇒ k=

4

48

⇒ k=12

I hop your doubt is clear now