If the locus of the image of the point λ 2 , 2 λ in the line mirror x - y + 1 = 0 (where λ is a parameter) is x - a 2 = b y - c where a , b , c ∈ I , then the value of a + b c + b is equal to

Step-by-step solution

Let, h , k be the image of the point λ 2 , 2 λ about the line x - y + 1 = 0 h - λ 2 1 = k - 2 λ - 1 = - 2 λ 2 - 2 λ + 1 2 h + 1 = 2 λ … . . i k = λ 2 + 1 … . . i i Put the value of λ from i in i i k - 1 = h + 1 2 2 ⇒ 4 y - 1 = x + 1 2 Hence, a = - 1 ,   b = 4 and c = 1