Question

The focal 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. $\{-2,\frac{1}{2}\}$
• D. $\{2,-\frac{1}{2}\}$

Answer 1

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

Here, the focal chord of $y^2=16x$ is tangent to circle $(x-6{)}^2+y^2=2$
$\Rightarrow$ Focus of parabola as $(a,0)$ i.e. $(4,0)$
Now, tangents are drawn from $(4,0)$ to $(x-6{)}^2+y^2=2$.
Since, $PA$ is tangent to circle.
$\therefore tan\theta$ = slope of tangent $=\frac{AC}{AP}=\frac{\sqrt{2}}{\sqrt{2}}=1$, or $\frac{BC}{BP}=-1$.

$\therefore$ Slope of focal chord as tangent to circle $=\pm 1$.