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Two perpendicular striaght lines through the focus of the parabola y2=4ax meets its directrix in T1 and T2 respectively. Show that the tangent the tangent to the parabola parallel to the perpendicular lines intersect in the midpoint of T1T2.
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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