Exam

JEE Advanced

Year

2010

Paper

Paper 1

Subject

Mathematics

Chapter

Parabola

JEE Advanced 2010 · Paper 1 · Mathematics · Parabola

Let A and B be two distinct points on the parabola y^2=4 x . If the...

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 $A B$ as its diameter, then the slope of the line joining $A$ and $B$ can be

Step-by-step solution

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