Question

if the locus of point of intersection of tangents to the parabola y^2=4ax which intecept a fixed length L on the directrix is (y^2-Kax) (x+a)^2=(Lx)^2
Then find the value of K.

Answer 1

K is an integer from 1 to 9

Answer 2

IITJEE integer type?

Answer 3

nope jst asked in my paper

Answer 4

the tangent is y=mx+a/m
the directrix is x=-a

let ur desired point be h,k

put in h,k into the tangent line

k = mh + a/m
m^2h -mk +a = 0

find the values of m from this quadratic

now solve both the lines with x+a=0

set the difference bgtw the y-coordinates as L