Mathematics - Parabola Question with Solution | TestHub

Here, coordinate $M=\left(\frac{t_1^2+t_2^2}{2},t_1+t_2\right)ie$, mid point of chord $AB$.
$MP=t_1+t_2=r$ Also, $m_{AB}=\frac{2t_2-2t_1}{t_2^2-t_1^2}=\frac{2^{\dots (i)}}{t_2+t_1}$ (when $AB$ is chord) $$\Rightarrow m_{AB}=\frac{2}{r}$$ [from Eq. (i)] Also, $m_{A^{\prime }{B}^{\prime }}=-\frac{2}{r}$ (when $A^{\prime }{B}^{\prime }$ is chord) Hence, (c, d) is the correct option.