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  • All chords of the parabola <img alt="y^2=4 x" src="https://entrancecorner.oncodecogs.

All chords of the parabola y^2=4 x  which subtend right angle at the origin are concurrent at the point:

Option: 1

(1,0)


Option: 2

(2,0)


Option: 3

(3,0)


Option: 4

(4,0)


Answers (1)

best_answer

Let y=m x+c  be such chord with extremities A \text { and } B \text {. }

The combined equation of the pair of lines

O A \text { and } O B \text { is } y^2-4 x\left(\frac{y-m x}{c}\right)=0

\begin{aligned} & \therefore \text { Coeff of } x^2+\text { Coeff of } y^2=0 \Rightarrow 1+\frac{4 m}{c}=0 \\ & \therefore c=-4 m \end{aligned}

\therefore \text { The chord equation is } y=m(x-4)

Posted by

Rishabh

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