Question

FIND THE RATIO IN WHICH THE LINE JOINING (-2,5) AND (-5,-6) IS DIVIDED BY THE LINE 2x + y = -4. HENCE FIND THE POINT OF INTERSECTION

Answer 1

Answer:

The variable line passing through point of intersection of x+2y−1=0 and 2x−y−1=0 is x+2y−1+λ(2x−y−1)=0

⇒(1+2λ)x+(2−λ)y−(1+λ)=0

the above line meets coordinate axes at A(

2λ+1

λ+1

,0) and B(0,

2−λ

λ+1

)

Let mid point of A and B is (x,y)

⇒2x=

2λ+1

λ+1

,2y=

2−λ

λ+1

⇒

2x

1

=

λ+1

2λ+1

...... (i)

⇒

2y

1

=

λ+1

2−λ

....... (ii)

3(i)+(ii) gives

2x

3

+

2y

1

=5

∴ Required locus is x+3y=10xy

Answer 2

Step-by-step explanation:

Find the ratio in which the line joining (-2, 5) and (-5,-6) is divided by the line 2x+y=-4. Hence find the point of intersection.