If one of a focal chord of the parabola,y^{2}=16x is at \left ( 1,4 \right ), then the length of this focal chord is :

  • Option 1)

    25

  • Option 2)

    22

  • Option 3)

    24

  • Option 4)

     20

 

Answers (1)

Equation of parabola

 y^{2}=16x

focus =\left ( a,0 \right )=\left ( 4,0 \right )

Slope =\frac{4-0}{1-4}=-\frac{4}{3}=tan \theta

Length of focal chord = 4\; a\; cosec^{2}\theta

                                    =4\times 4\times \frac{25}{16}=25


Option 1)

25

Option 2)

22

Option 3)

24

Option 4)

 20

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