Consider the region R= \ (x, y) R R : x 0 . and .y^ 2 4-x \ . Let F be the family of all circles that are contained in R and have centers on the x-axis. Let C be the circle that has largest radius among the circles in F . Let ( , ) be a point where the circle C meets the curve y^ 2 =4-x. The value of α is _____.
A. A
equation of normal at P is y - β = 2 β x - 4 + β 2 Passing through ( r , 0 ) ⇒ - 1 = 2 r - 4 + β 2   . . . i or    β = 0   . . . i i Also r 2 = r + β 2 - 4 2 + β 2   . . . i i i from i and i i i r = 3 2 , - 5 2 so radius of circle is 1 . 5 and α = 2 from i i and i i i r = 2 but in this case circle intersect at three points
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