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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 .

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

Grade:11

1 Answers

Nishant Vora IIT Patna
askIITians Faculty 2467 Points
5 years ago
Take the slopes of 2 perpendicular SL as m and -1/m

Now 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 = -a

Once 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 do

Thanks

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