- The hyperbola \(H\) has Cartesian equation \(x y = 25\)
The parabola \(P\) has parametric equations \(x = 10 t ^ { 2 } , y = 20 t\)
The hyperbola \(H\) intersects the parabola \(P\) at the point \(A\)
- Use algebra to determine the coordinates of \(A\)
The point \(B\) with coordinates \(( 10,20 )\) lies on \(P\)
- Find an equation for the normal to \(P\) at \(B\)
Give your answer in the form \(a x + b y + c = 0\), where \(a , b\) and \(c\) are integers to be determined.
- Use algebra to determine, in simplest form, the exact coordinates of the points where this normal intersects the hyperbola \(H\)
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