Question

If the length of double ordinate of parabola y²=4ax is 8a then prove that the lines meeting the double ordinate from the origin are perpendicular?

Answer 1

double ordinate is perpendicular to axis of parabola
so, the end points be
P(at²,2at) and P'=(at²,-2at)
pp'=8a
root of (4at)²=8a
t=2
∴P=(at²,2at)=(4a,4a)
P'=(at²,-2at)=(4a,-4a)
vertex is O(0,0)
slope of OP=m₁=4a-0/(4a-0)=1
slope of OP'=m₂=4a-0/(-4a-0)=-1
m₁ X m₂ =1 X (-1)
 = -1
∴the line joining the origin to double ordinate will be perpendicular to each other.