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Vanya Saxena Grade: Upto college level
        

If two tangents to the parabola y2=4ax form a point P make angles θ1 and theta 2 with the axis of parabola then find the locus of point P such that theta1+theta2=pi/2

7 years ago

Answers : (2)

Badiuddin askIITians.ismu Expert
147 Points
										

Dear vanya saxena


tangent at parabola at (at12,2at1)  is yt1 =x+at12


so tangebt at (at22,2at2)  is yt2 =x+at22


these tangent meat at point P


so point p is


{at1t2,a(t1 +t2)}


 


also  tan Θ1 =1/t1


      tanΘ 2 =1/t2


and tan(Θ1 + Θ2) = tan pi/2


simplify


so t1t2 =1


locus of point p


x=at1t2


x=a


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Badiuddin




 

7 years ago
sunny redu
24 Points
										
as in the given question the two tangents are perpendicular  and the locus of perpendicular tangents is director circle and in case of parabola director circle is directrix and in the question directrix is x=a which is is required locus
22 days ago
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