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Two perpendicular striaght lines through the focus of the parabola y 2 =4ax meets its directrix in T 1 and T 2 respectively. Show that the tangent the tangent to the parabola parallel to the perpendicular lines intersect in the midpoint of T 1 T 2 .
Take the slopes of 2 perpendicular SL as m and -1/mNow write eqn of both lines as it passes through focus (a,0).Now we can get T1 and T2 both points as they are intersection of Lines with directix x = -aOnce you getT1 and T2 then you can find its midpoint also.Finally you need to write eqn of tangents and find its intersection point.I have given you all the steps , calculation you can doThanks
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