See image — AITS & Test Series Chemistry Question

💡 Solution & Explanation

Solving H and L we get 2 2x 2x 1 0    let the roots be  and  1  and 1 . 2  Let points of intersection are     A , 1 and B , 1   Family of circles passing through A and B is     2 2 x y x 1 y 1 1 0     ∵ this circle touches at   A , 1  ∴ AC A dy m 1, dx        where A dy dx       is slope of hyperbola at A and AC m is slope of line joining A and centre of circle C. AC A dy 2 1 2 and m dx 3 1 2             AC A dy 2 1 2 m 1 1 dx 3 1 2                2 1 5 10 5      ∴ circle: 2 2 x y 4x 4y 6 0       2 R 14 