Question

factorise 4+x²+9y²+4x-6xy-12y
​

Answer 1

Answer:

Let lx+my+c

1

=0 & lx+my+c

2

=0

be two parallel lines represented by the given equation then we have

ax

2

+2hxy+by

2

+2gx+2fy+c=(lx+my+c

1

)(lx+my+c

2

)

On comparing

a=l

2

,b=m

2

,2h=2lm,l(c

1

+c

2

)=2g

and m(c

1

+c

2

)=2f,c

1

c

2

=c

Now distance between the parallel lines

=

l

2

+m

2

∣c

1

−c

2

∣

=

l

2

+m

2

(c

1

+c

2

)

2

−4c

1

c

2

=

a+b

(

l

2g

)

2

−4c

=

a+b

a

4g

2

−4c

=2

a(a+b)

g

2

−ac

i. e. Reason (R) is false

Again x

2

+6xy+9y

2

+4x+12y−5=0

are two parallel lines given by (x+3y−1)(x+3y+5)=0

i.e. x+3y−1=0 & x+3y+5=0

and distance between them

=2

a(a+b)

g

2

−ac

=2

1(1+9)

4+5

=

10

6

so the Assenion (A) is true As Assertion (A) is true & Reason (R) is false,