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  • Let A and B be two distinct points on the parabola    . If the axis of the parabola

Let A and B be two distinct points on the parabola  y^2=4 x  . If the axis of the parabola touches a circle of  radius r having AB as its diameter, then the slope of the line joining A and B can be? 

Option: 1

\begin{aligned} & -\frac{1}{r} \\ \end{aligned}


Option: 2

\frac{1}{r} \\


Option: 3

\frac{2}{r} \\


Option: 4

-\frac{2}{r}


Answers (1)

best_answer

Here, coordinate  M=\left(\frac{t_1^2+t_2^2}{2}, t_1+t_2\right)  , i.e. midpoint of chord AB.

M P=t_1+t_2=r \\.......................(i)

\begin{aligned} & M P=m_{A B}=\frac{2 t_2-2 t_1}{t_2^2-t_1^2}=\frac{2}{t_2+t_1} \text { (when } \mathrm{AB} \text { is chord) } \\ & \Rightarrow m_{A B}=\frac{2}{r} \end{aligned}...........from eq (i)

 

Posted by

himanshu.meshram

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