Question

The focal chord to $y^2=16x$ is tangent to $(x-6{)}^2+y^2=2$. Then the possible value of the slope of this chord is

• A. $\{-1.1\}$
• B. $\{-2,2\}$
• C. $\{-2,1/2\}$
• D. $\{2,-1/2\}$

Answer 1

Answer: (A)

For the parabola $y^2=16x$, focus is $(4,0)$. Let $m$ be the slope of focal chord. Then the equation is
$y=m(x-4)$ ... (1)
Given that the above line is a tangent to the circle $(x-6{)}^2$ $+y^2=2$ for which the centre is $C(6,0)$ and radius $r$ is $\sqrt{2}$. Therefore, the length of perpendicular from $(6,0)$ to $(1)$ is $r$.
Therefore,
$\frac{|6m-4m|}{\sqrt{m^2+1}}=\sqrt{2}$
or $2m^2=m^2+1$
or $m^2=1$
or $m=\pm 1$