1) Try to find the circular equation through three known points （1,1）（2,-1）（3,2） 2) A circle and two parallel lines 2x + y = 5 are tangent to 2x + y + 15 = 0 and pass through point (2,1) Find the equation for this circle 3) A circle passes through (1,1) and (1, - 1) and is tangent to the straight line X - 2 = 0. Find the equation of the circle 4) Try to find the parameter equation of circle x ^ 2 + y ^ 2-x-3y = 0 5) Try to find the circular equation with the diameter of the line between (2, - 5) and (8, - 1), and find the parametric equation of this circle 20 points for answering one question | Math enthusiast | Mathematical art

1) Try to find the circular equation through three known points （1,1）（2,-1）（3,2） 2) A circle and two parallel lines 2x + y = 5 are tangent to 2x + y + 15 = 0 and pass through point (2,1) Find the equation for this circle 3) A circle passes through (1,1) and (1, - 1) and is tangent to the straight line X - 2 = 0. Find the equation of the circle 4) Try to find the parameter equation of circle x ^ 2 + y ^ 2-x-3y = 0 5) Try to find the circular equation with the diameter of the line between (2, - 5) and (8, - 1), and find the parametric equation of this circle 20 points for answering one question

1) Let the circular equation be X & sup2; + Y & sup2; + DX + ey + F = 0, and the coordinates of three points (1,1) (2, - 1) (3,2) be substituted into D + e + F = - 22d-e + F = - 53d + 2E + F = - 13. The simultaneous solutions of the equations are d = - 5, e = - 1, f = 4. So the circular equation is X & sup2; + Y & sup2; - 5x-y + 4 = 02

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