If the common tangent to the parabolas, y 2 = 4 x a n d x 2 = 4 y also touches the circle, x 2 + y 2 = c 2 , then c is equal to :

Step-by-step solution

Given: y 2 = 4 x & x 2 = 4 y Comparing with standard equations, y 2 = 4 a 1 x   &   x 2 = 4 a 2 y , a 1 = a 2 = 1 Therefore tangent of y 2 = 4 x is y = m x + 1 m which is also tangent to x 2 = 4 y , whose equation would be y = m x - m 2 ∴    1 m = - m 2 ⇒    m = - 1 ∴ common tangent is y = - x - 1 , which touches x 2 + y 2 = c 2 ∴   ( - 1 ) 2 = c 2 ( 1 + ( - 1 ) 2 ) ⇒   1 = c 2 · ( 1 + 1 ) ⇒ c 2 = 1 2