Question

A circle of radius 4, drawn on a chord of the parabola $y^2=8x$ as diameter, touches the axis of the parabola. Then, the slope of the chord is

• A. $\frac{1}{2}$
• B. $\frac{3}{4}$
• C. $1$
• D. $2$

Answer 1

Answer: (C)

$1$

Let A and B be on the parabola.
A$(\frac{y_1^2}{8},y_1)$ and B be $(\frac{y_2^2}{8},y_2).$
$\therefore$ centre O is midpoint of AB.
So, O is $(\frac{y_1^2+y_2^2}{16},\frac{y_1+y_2}{2})$ and
Since, $r=4$
So, $\frac{y_1+y_2}{2}=4$
$\Rightarrow y_1+y_2=8$
Slope of AB $=\frac{y_2-y_1}{\frac{y_2^2-y_1^2}{8}}$
$=\frac{8}{y_2+y_1}=\frac{8}{8}$
So, slope $=1.$