Question

If slope of the focal chord of parabola $y^2=8x$ is the greater root of the equation $x^2-6x+8=0$, then length of the focal chord will be

• A. $10$ units
• B. $17$ units
• C. $\frac{17}{4}$ units
• D. $\frac{17}{2}$ units

Answer 1

The correct option is D $\frac{17}{2}$ units

$x^2-6x+8=0$
Roots are $2$ and $4.$
Slope $=\tan \alpha =4$
$\Rightarrow {\text{cosec}}^2\alpha =\frac{17}{16}$
$a=2$
Now length of focal chord is $4a{\text{cosec}}^2\alpha =4\times 2\times \frac{17}{16}$
$=\frac{17}{2}$ units