In the figure below, A B is diameter with coordinate A(3,2) and B(-5,4) of circle ABC. M is the

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In the figure below, \( \overline{A B} \) is diameter with coordinate \( A(3,2) \) and \( B(-5,4) \) of circle \( \mathrm{ABC} \). M is the center of the circle. \( \overline{B C} \) produced meets AT in T. \( N(2,-2) \) is the point on the line \( \overline{T A} \). \( \mathrm{C} \) is on the \( \mathrm{y} \) axis intercepts on the circle. (a) Determine the coordinate of \( \mathrm{M} \) (the center of the circle) (b) Write down the equation of the circle. (c) Prove that TA is tangent to the circle at A. (d) Determine the equation of the line \( \overline{T A} \) and \( \overline{B T} \)

          In the figure below, \( \overline{A B} \) is diameter with coordinate \( A(3,2) \) and \( B(-5,4) \) of circle \( \mathrm{ABC} \). M is the center of the circle. \( \overline{B C} \) produced meets AT in T. \( N(2,-2) \) is the point on the line \( \overline{T A} \). \( \mathrm{C} \) is on the \( \mathrm{y} \) axis intercepts on the circle.
(a) Determine the coordinate of \( \mathrm{M} \) (the center of the circle)
(b) Write down the equation of the circle.
(c) Prove that TA is tangent to the circle at A.
(d) Determine the equation of the line \( \overline{T A} \) and \( \overline{B T} \)

In the figure below, A B is diameter with coordinate A(3,2) and B(-5,4) of circle ABC. M is the center of the circle. B C produced meets AT in T. N(2,-2) is the point on the line T A. C is on the y axis intercepts on the circle.
(a) Determine the coordinate of M (the center of the circle)
(b) Write down the equation of the circle.
(c) Prove that TA is tangent to the circle at A.
(d) Determine the equation of the line T A and B T

Added by Nerea K.

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