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Algebra: Slopes and Circles

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Three points 4(2,3), B(-1, -2) and C(-1,6) and the circle that. passes through them.
(a) (i) Find the slope of the line that passes through A and B.
(ii) Find the coordinates of the midpoint of the line segment AB.
(iii) Find the equation of the perpendicular bisector of AB.
(iv) Show that the line corresponding to the parametric equations x=t?2, y=?(3/5)t+2
is the same line as in part (a)(iii) above.
(b) Find the equation of the perpendicular bisector of the line segment AC.
(c) (i) From your answers to parts (a)(iv) and (b), find the centre of the circle that passes through A. B and C.
(ii) Find the radius of this circle, giving your answer correct to two decimal places.
(iii) Write down the equation of the circle.


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