question_answer

The slopes of the focal chords of the parabola\[{{y}^{2}}=32x,\] which are tangents to the circle \[{{x}^{2}}+{{y}^{2}}=4\] are ________.

A)  \[\frac{1}{\sqrt{3}},\frac{-1}{\sqrt{3}}\]            

B)  \[\frac{1}{\sqrt{15}},\frac{-\,1}{\sqrt{15}}\]

C)  \[\frac{2}{\sqrt{15}},\frac{-\,2}{\sqrt{15}}\]                  

D)  \[\frac{1}{\sqrt{2}},\frac{-\,1}{\sqrt{2}}\]

E)  None of these