Let the equation x 2 + y 2 + px + (1 p)y + 5 = 0 represent circles of varying radius r (0, 5]. Then the number of elements in the set S = q : q = p 2 and q is an integer ...

r = p^2 4 + (1 - p)^2 4 - 5 = 2p^2 - 2p - 19 2 Since, r (0,5] So, 0 < 2p^2 - 2p - 19 100 p [ 1 - 239 2,1 - 39 2 ) ( 1 + 39 2,1 + 239 2 ] so, number of integral values of p 2 is 61....

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Let the equation x2 y2 px 1 py 5 0 represent circles of vary: null (Mathematics) | DivineJEE

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Mathematics

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Mathematics

Let the equation x² + y² + px + (1

-

p)y + 5 = 0 represent circles of varying radius r

\in

(0, 5]. Then the number of elements in the set S = {q : q = p² and q is an integer} is __________.

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