JEE Main20199 Apr 2019Morning ShiftMathematicsParabolaActual
If one end of a focal chord of the parabola, y 2 = 16 x is at 1 , 4 , then the length of this focal chord is
Options
- A24
- B25
- C22
- D20
Correct answer
B. 25
Step-by-step solution
The given parabola y 2 = 16 x is of the form y 2 = 4 a x , hence a = 4 and the focus of the parabola is a ,   0 = 4 ,   0 . The equation of a line joining the points x 1 ,   y 1 and x 2 ,   y 2 is y - y 1 = y 2 - y 1 x 2 - x 1 x - x 1 . Therefore, equation of chord joining P 1 ,   4 to focus S 4 ,   0 is y - 0 = - 4 3 x - 4 ⇒ 3 y = - 4 x + 16 ⇒ 4 x   + 3 y - 16 = 0 To find the points where this line will cut the parabola put x = y 2 16 from the parabola into the line,