Question

transform the following equation into the form L1+lemada L2=0 and find the point of concurrency of (k+1)x+(k+2)y+5=0​

Answer 1

Given : A family of equations is (k + 1)x + (k + 2)y + 5 = 0

To find : transform the above equation into the form L₁ + λL₂ = 0 and find the point of concurrency of (k + 1)x + (k + 2)y + 5 = 0

solution : here (k + 1)x + (k + 2)y + 5 = 0

⇒kx + x + ky + 2y + 5 = 0

⇒k(x + y) + (x + 2y + 5) = 0

⇒(x + 2y + 5) + k(x + y) = 0 this is in the form of L₁ + λL₂ = 0

now, L₁ : x + 2y + 5 = 0

L₂ : x + y = 0

the point of concurrency is point of intersection of L₁ and L₂.

solve the equation (x + 2y + 5) = 0 and (x + y) = 0

(x + 2y + 5) - (x + y) = 0

⇒y + 5 = 0

⇒y = - 5

and x = 5

Therefore the point of concurrency is (5, -5)

Answer 2

Step-by-step explanation:

point of concurrency is (5,-5)