Home
Class 11
MATHS
AB, AC are tangents to a parabola y^(2)=...

AB, AC are tangents to a parabola `y^(2)=4ax`. If `l_(1),l_(2),l_(3)` are the lengths of perpendiculars from A, B, C on any tangent to the parabola, then

A

`l_(1), l_(2), l_(3)` are in GP

B

`l_(2), l_(1), l_(3)` are in GP

C

`l_(3), l_(1), l_(2)` are in GP

D

`l_(3), l_(2), l_(1)` are in GP

Text Solution

Verified by Experts

The correct Answer is:
B, C
Let the coordinates of B C be `(at_(1)^(2), 2at_(1))` and `(at_(1)t_(2), a(t_(1)+t_(2))` respectively. Then, the coordinates of A are `(at_(1)t_(2), a(t_(1)+t_(2))`
The equation of any tangent to `y^(2)=4ax` is `ty=x+aty^(2)`
`:." "l_(1)=(at_(1)t_(2)-a(t_(1)-t_(2))t+at^(2))/(sqrt(1+t^(2)))`
Clearly, `l_(2)l_(3)=l_(1)^(2)`. Therefore, `l_(2)l_(1)l_(3)` are om G.P.
Promotional Banner

Similar Questions

Explore conceptually related problems

AB,AC are tangents to a parabola y^(2)=4ax;p_(1),p_(2),p_(3) are the lengths of the perpendiculars from A,B,C on any tangents to the curve,then p_(2),p_(1),p_(3) are in:

Equation of tangent to parabola y^(2)=4ax

The feet of the perpendicular drawn from focus upon any tangent to the parabola,y=x^(2)-2x-3 lies on

If the line px+qy=1 is a tangent to the parabola y^(2)=4ax. then

If the line px + qy =1 is a tangent to the parabola y^(2) =4ax, then

The locus of foot of the perpendiculars drawn from the vertex on a variable tangent to the parabola y^(2)=4ax is

T is a point on the tangent to a parabola y^(2) = 4ax at its point P. TL and TN are the perpendiculars on the focal radius SP and the directrix of the parabola respectively. Then

Statement-1: y+b=m_(1) (x+a) and y+b=m_(2)(x+a) are perpendicular tangents to the parabola y^(2)=4ax . Statement-2: The locus of the point of intersection of perpendicular tangents to a parabola is its directrix.