Let y = p x be the parabola passing through the points – 1 ,   0 ,   0 ,   1 and 1 ,   0 . If the area of the region x ,   y : x + 1 2 + y - 1 2 ≤ 1 ,   y ≤ p x is A , then 12 π - 4 A is equal to ________ .

Step-by-step solution

Let, the parabola be y = a x 2 + b x + c , Now given parabola is passing through - 1 , 0 ,   0 , 1   &   1 , 0 Now putting the value in the above equation of parabola we get, a - b + c = 0   . . . . . . 1 , c = 1     . . . . 2 and   a + b + c = 0   . . . . 3 Now solving above three equations we get, Parabola as y = 1 - x 2 Now area of region between y = 1 - x 2 and x + 1 2 + y - 1 2 ≤ 1 is given by, Now from above diagram, required area will be, A = ∫ - 1 0 -