Question

Find the angle between the lines joining the origins to the points pt Intersection of the curve x²+2xy+3y²+4x+8y-11=0 and the line 3x-y+2=0​

Answer 1

Answer:

substitute y=mx in x−y=2

we get,

x=

1−m

2

,y=

1−m

2m

substitute these values in equation, x

2

−4xy+2y

2

−2x+y+k=0

(

1−m

2

)

2

−4

1−m

2

1−m

2m

+2(

1−m

2m

)

2

−2

1−m

2

+

1−m

2m

+k=0

solving the above equation, we get,

(k+6)m

2

−(2k+10)m+k=0..........(1)

m=

k+6

k+5±

4k+25

m

1

−m

2

=

k+6

2

4k+25

..........(2)

m

1

m

2

=

k+6

k

........(3)

since given,

lines making an angle of 45

∘

∣

∣

∣

∣

∣

1+m

1

m

2

m

1

−m

2

∣

∣

∣

∣

∣

=1

(m

1

−m

2

)

2

=(1+m

1

m

2

)

2

From (2) and (3)

(

k+6

2

4k+25

)

2

=(1+

k+6

k

)

2

solving the above equation we get

k=−1±

17