Question

The ford chord to $y^2=16x$ is tangent to ${(x-6)}^2+y^2=2$ then the possible values of the slope of this chord are

• A. $\{-1,1\}$
• B. $\{-2,2\}$
• C. $\{-2,1/2\}$
• D. $\{2,-1/2\}$

Answer 1

The correct option is A $\{-1,1\}$

Focus of parabola $=(4,0)$

$\therefore \frac{y-0}{x-4}=m\Rightarrow mx-y-4m=0$ is the focal choral .

Now of this is tangent to given circle,then its distance from centre $(6,0)$ is equal to radius $\left(\sqrt{2}\right)$

$\therefore \left|\frac{6m-4m}{\sqrt{1+m^2}}\right|=\sqrt{2}$

$4m^2=2(1+m^2)$

$2m^2=2$

$m^2=1$

$\therefore m=\pm 1$