A circle passes through the points \(D(-4,-3)\) and \(E(4,-7)\).
The line with equation \(4y=3x-15\) is a normal to the circle at a point \(F\).
Showing all your working, find the equation of the circle.[7]
Explain why the point \((-1,1)\) lies inside the circle.[2]
The line \(y=x-3\) intersects the circle at points \(P\) and \(Q\). Determine, with working, whether the line segment \(PQ\) is a possible diameter of the circle.[2]
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Answer:(a) \((x-1)^2+(y+3)^2=25\); (b) distance squared \(20<25\); (c) \(PQ\) is not a diameter.