- The point \(A\) has coordinates \(( 2,5 )\) and the point \(B\) has coordinates \(( - 2,8 )\). Find, in cartesian form, an equation of the circle with diameter \(A B\).
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\caption{Figure 1}
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The circle \(C\), with centre \(( a , b )\) and radius 5 , touches the \(x\)-axis at \(( 4,0 )\), as shown in Fig. 1.
- Write down the value of \(a\) and the value of \(b\).
- Find a cartesian equation of \(C\).
A tangent to the circle, drawn from the point \(P ( 8,17 )\), touches the circle at \(T\).
- Find, to 3 significant figures, the length of \(P T\).