Question

Length of the sub-tangent at any point P(x, y) on the parabola $y^2=4ax$ equals _____ the abscissa of the point P

• A. Twice
• B. thrice
• C. half
• D. one - third

Answer 1

The correct option is A

Twice

Given parabola is a standard parabola $y^2=4ax$

coordinates of point $P=(a{t}^2,2at)$

Equation of tangent at point P

$y.2at=2a(x+a{t}^2)$

$yt=x+a{t}^2$ ...............(1)

Intersection of tangent at x-axis

y=0

$0=x+a{t}^2$

$x=-a{t}^2$

Coordinates of point $T(-a{t}^2,0)$

Coordinates of point $D=(a{t}^2,0)$

$TD=\sqrt{(a{t}^2+a{t}^2{)}^2+0}$

$TD=2a{t}^2$

$OD=a{t}^2$

$TD=2\times OD$

So,length of subtangent at any point P(x,y) on

the parabola $y^2=4ax$ equals twice the abscissa of the

point P.