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QUESTION 4 In the diagram, the circle centred at \( \mathrm{M}(a ; b) \) is drawn. \( \mathrm{T} \) and \( \mathrm{R}(6 ; 0) \) are the \( x \)-intercepts of the circle. A tangent is drawn to the circle at \( \mathrm{K}(5 ; 7) \). 4.1 \( \mathrm{M} \) is a point on the line \( y=x+1 \). 4.1.1 Write \( b \) in terms of \( a \). 4.1.2 Calculate the coordinates of \( \mathrm{M} \). 4.2.2 TR form \( y=m x+c \). 4.4 A horizontal line is drawn as a tangent to the circle \( \mathrm{M} \) at the point \( \mathrm{N}(c ; d) \), where \( d<0 \). 4.4.1 Write down the coordinates of \( \mathrm{N} \). 4.4.2 Determine the equation of the circle centred at \( \mathrm{N} \) and passing through \( \mathrm{T} \). Write your answer in the form \( (x-a)^{2}+(y-b)^{2}=r^{2} \). \( [20] \)

          QUESTION 4
In the diagram, the circle centred at \( \mathrm{M}(a ; b) \) is drawn. \( \mathrm{T} \) and \( \mathrm{R}(6 ; 0) \) are the \( x \)-intercepts of the circle. A tangent is drawn to the circle at \( \mathrm{K}(5 ; 7) \).
4.1 \( \mathrm{M} \) is a point on the line \( y=x+1 \).
4.1.1 Write \( b \) in terms of \( a \).
4.1.2 Calculate the coordinates of \( \mathrm{M} \).
4.2.2 TR form \( y=m x+c \).
4.4 A horizontal line is drawn as a tangent to the circle \( \mathrm{M} \) at the point \( \mathrm{N}(c ; d) \), where \( d<0 \).
4.4.1 Write down the coordinates of \( \mathrm{N} \).
4.4.2 Determine the equation of the circle centred at \( \mathrm{N} \) and passing through \( \mathrm{T} \). Write your answer in the form \( (x-a)^{2}+(y-b)^{2}=r^{2} \).
\( [20] \)

QUESTION 4
In the diagram, the circle centred at M(a ; b) is drawn. T and R(6 ; 0) are the x-intercepts of the circle. A tangent is drawn to the circle at K(5 ; 7).
4.1 M is a point on the line y=x+1.
4.1.1 Write b in terms of a.
4.1.2 Calculate the coordinates of M.
4.2.2 TR form y=m x+c.
4.4 A horizontal line is drawn as a tangent to the circle M at the point N(c ; d), where d<0.
4.4.1 Write down the coordinates of N.
4.4.2 Determine the equation of the circle centred at N and passing through T. Write your answer in the form (x-a)^2+(y-b)^2=r^2.
[20]

Added by David C.

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