exam Maths Puzzle Numerical Ability

Write the equation of a circle with a diameter having endpoints at (-2,6) and (8,4).

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Determine whether the following equations have a solution or not? Justify your answer.

1/2y2 - 4y - 7(3)1/2 = 0
2x2 - 10x + 25 = 0
2x2 - 6x + 5 = 0
s2 - Solve {{{cos2x=sqrt(2)/2}}} in an algebraic manner and state the general solutions.

Thanks for your help.