Question

If (1/2, 2) is one extremity of a focal chord of the parabola y² = 8x. Find the coordinates of the other extremity. 

Answer 1

Given parabola y² = 8x 

focus S= (2,0) 

One end of the focal chord is

  

Let Q (x , y ) = (x₁,y₁) be the other end of the focal chord. 

Q is a point on the parabola,

Slope of SP=

Slope of SQ=

PSQ is a focal chord ⇒ the points P, S, Q are collinear. 

Therefore, Slope of SP = Slope of SQ  

Therefore (8, –8) other extremity. 

(If x₁= 1/2 then y₁ =2 which is the given point .)