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  • If one end of a focal chord of the parabola,  is at (1, 4), then the length of this focal c

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

Option: 1

22


Option: 2

25


Option: 3

24


Option: 4

20


Answers (1)

best_answer

Equation of given parabola is y^2=16 x , its focus is (4,0)

Since, slope of line passing through \left(x_1, y_1\right) \text { and }\left(x_2, y_2\right) is given by

m=\tan \theta=\frac{y_2-y_1}{x_2-x_1}

 ∴ Slope of focal chord having one end point is (1,4) is

m=\tan \alpha=\frac{4-1}{1-4}=\frac{4}{3}

where, ‘α’ is the inclination of the focal chord with X-axis.

Since, the length of focal chord = 4 a \cdot \operatorname{cosex}^2 \alpha

∴ The required length of the focal chord = 

\begin{aligned} & =16\left[1+\cot ^2 \alpha\right] \\ & \because \cot \alpha=\frac{1}{\tan \alpha}=\frac{-3}{4} \\ & \therefore 16\left[1+\frac{9}{16}\right]=25 \text { units } \end{aligned}

The graphs of y^2=16 x is 

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Divya Prakash Singh

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