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18

Show that the point (x, y) given by and lies on a circle for all real values of t such that - 1 ≤ t ≤ 1, where a is any given real number.

12

Find the equations of the circles which pass through the origin and cut off equal chords of √2 units from the lines y = x and y = - x.

19

The equation of the circle which touches the axes of coordinates and the line and whose centres lie in the first quadrant is x^{2} + y^{2} – 2cx – 2cy + c^{2} = 0, where c is equal to