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  • A chord of slope of the circle <img alt="\mathrm{x^{2}+y^{2}=2}" src="https://entrancecorner.

A chord of slope \mathrm{'m'} of the circle \mathrm{x^{2}+y^{2}=2} touches the parabola \mathrm{y^{2}=8 x}, then set of values of \mathrm{m} is given by

Option: 1

(-\infty, \infty)


Option: 2

(-1,1)


Option: 3

(0, \infty)


Option: 4

(-\infty,-1) \cup(1, \infty)


Answers (1)

Equation of tangent to the parabola with slope \mathrm{'m'} is \mathrm{y=m x+\frac{2}{m}} This line to be chord of the circle \mathrm{x^{2}+y^{2}=2},

If \mathrm{\left|\frac{2}{\frac{m}{\sqrt{1+m^{2}}}}\right|<\sqrt{2}}
\mathrm{\Rightarrow \quad 4<\left(\mathrm{m}^{4}+\mathrm{m}^{2}\right) \cdot 2}

\mathrm{\Rightarrow \quad \mathrm{m}^{4}+\mathrm{m}^{2}-2>0}
\mathrm{\Rightarrow \mathrm{m}^{2}-1>0}

i.e. m \in(-\infty,-1) \cup(1, \infty)
 

Posted by

Kshitij

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