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  • If a focal chord with positive slope of the parabola touches the circle 

If a focal chord with positive slope of the parabola \mathrm{y^2 = 16x} touches the circle 

\mathrm{x^2+y^2-12 x+34=0}, then m is 

 

Option: 1

\mathrm{\sqrt{3}}


Option: 2

1


Option: 3

2


Option: 4

\frac{1}{2}


Answers (1)

best_answer

Any tangent to circle will be 

 \mathrm{y=m(x-6) \pm \sqrt{2} \sqrt{1+m^2}}

If it is a focal chord to parabola, then

\mathrm{\begin{aligned} & \text { I } 0=m(4-6) \pm \sqrt{2} \sqrt{1+m^2} \\ & \Rightarrow \quad m= \pm 1 \text {, so } m=1 \end{aligned}}

Hence answer is (b).


 

 

 

Posted by

mansi

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