The point of intersection of the lines which are common tangent to both the curves y = x 2 and x 2 + y + 1 = 0 is

Step-by-step solution

For y = x 2 , equation of the tangent is y = m x - m 2 4 For this line to be tangent to x 2 + y + 1 = 0 ⇒ x 2 + m x - m 2 4 + 1 = 0 will have D = 0 ⇒ m 2 + 4 m 2 4 - 1 = 0 ⇒ m = ± 2 ⇒ Tangents are y = 2 x - 1 2 and y = - 2 x - 1 2 ⇒ Point of intersection of the tangents is 0 , - 1 2