IIT JEE , AIEEE Forum - Mathematics , Analytical Geometry

VIM

If the focal distance of a point on a parabola y² = 4x is 6, then the coordinates of the point are
(a) (5, 2 ROOT 5) (b) (5, -2ROOT5) (c) (5, ROOT5) (d) none of these

abhijeet_0201

let coordinates be (x,y)

focus =(1,0)

focal dis=

(x-1)²+y²

putting y²=4x

d^2 =(x-1)²+4x

36=x²+2x+1

solving

x=5 or -7

since -7 does not lie on the parabola

so x=5

y=

20=+-2root5

so (a) and (b)

elessar_iitkgp

Good work @abhijeet_0201

priyesh

focal distance = distance from directrix

directrix equation is x = -1
so distance of point from directrix is given as 6
hence x coordinate is 5

so y^2 = 4(5)
=> y = +- 2root(5)

Ask & Discuss Questions with Community & Experts