I = 1, 2, 3, 4 respectively origin 'O' being the centre of the four hyperbola Now match the entries from the following two columnsLet us define the "size" of a positive integer solution (x,y,z) to be x y ∈ Z The number of pairs of real numbers (x,y) that satisfy 2x2 y2 2xy− 2y 2 = 0 HInt 2x2 x(2y)y2 −2y2 = 0 As x is real, the discriminant must be ≥ 0 (2y)2 −8(y2 −2y 2) ≥ 0 0 ≥ −4(y− 2)2 (y− 2)2 ≤ 0 But as y is real, (y −2)2 ≥ 0 Let the tangent to the circle x2 y2 = 25 at the point R (3, 4) meet xaxis and yaxis at point P and Q, respectively If r is the radius of the circle passing through the origin O and having centre at the incentre of the triangle OPQ, then r2 is equal to (1) 529 64 529 64 (2) 125 72 125 72 (3) 625 72 625 72 Art Of Problem Solving Let the circle (x-1)^2+(y-2)^2=25
