Question

If focal chord to $y^2=16x,$ is tangent to $(x-6{)}^2+y^2=2,$ then a possible value of the slope of this chord is

• A. $-1$
• B. $5$
• C. $-2$
• D. $1/2$

Answer 1

Answer: (A)

$-1$

If focal chord to $y^2=16x$ is tangent to $(x-6{)}^2+y^2=2$

Then a possible value of slope of this chord will be

Focus of $y^2=16x$ is $(4,0)$

Equation of focal chord is

$y=m(x-4)........\left(1\right)$

Perpendicular distance of (1) from center of circle $(6,0)$ is $\sqrt { 2 } $

$\frac{|6m-4m-0|}{\sqrt{m^2+1}}=\sqrt{2}(2m{)}^2=2(m^2+1)2m^2=2m=1,-1$