Tangent and normal and tangent

Geometry Level 4

The tangent and normal at the point P = ( a t 2 , 2 a t ) P=(at^2,2at) to the parabola y 2 = 4 a x y^2=4ax meet the x x -axis in T T and G G respectively, then the angle at which the tangent at P P to the parabola is inclined to the tangent at P P to the circle through P , T P,T and G G is equal to __________ \text{\_\_\_\_\_\_\_\_\_\_} .

arctan ( t 2 ) \arctan(t^2) arccot t \text{arccot} t arccot ( t 2 ) \text{arccot}(t^2) arctan ( 2 a t ) \arctan(2at) arccot ( 2 a t ) \text{arccot}(2at) arccot ( a 2 t ) \text{arccot}(a^2 t) arctan t \arctan t arctan ( a 2 t ) \arctan(a^2 t)

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