Let the quadratic curve passing through the point - 1 , 0 and touching the line y = x at 1 , 1 be y = f x . Then the x -intercept of the normal to the curve at the point α , α + 1 in the first quadrant is

Step-by-step solution

Given, The quadratic curve passing through the point - 1 , 0 and touching the line y = x at 1 , 1 be y = f x , Now let the curve be y = a x 2 + b x + c Passes through - 1 , 0 ⇒ a - b + c = 0     . . . . i Passes through 1 ,   1 ⇒   a + b + c   =   1   . . . . . … i i Now given tangent to y = x at 1 , 1 , So, d y d x = 1 ⇒     2 a + b   =   1   . . . . … i i i Solving all above three equations we get, a = 1 4 ,   b = 1 2 a