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JEE Main & Advanced Sample Paper JEE Main Sample Paper-27

  • question_answer
    A chord is drawn through the focus of parabola \[{{y}^{2}}=6x\] such that its distance from the vertex of this parabola is \[\frac{\sqrt{5}}{2}\], then its slope can be

    A)  \[\frac{\sqrt{5}}{2}\]                            

    B)  \[\frac{\sqrt{3}}{2}\]

    C)  \[\frac{2}{\sqrt{5}}\]                            

    D)  \[\frac{2}{\sqrt{3}}\]

    Correct Answer: A

    Solution :

    Let equation of line is \[(y-0)=m\left( x-\frac{3}{2} \right)\] \[\Rightarrow \,\,\,2mx-2y-3m=0\] Now, \[\frac{|3m|}{2\sqrt{1+{{m}^{2}}}}\,=\frac{\sqrt{5}}{2}\] \[\Rightarrow \,\,9{{m}^{2}}=5{{m}^{2}}+5\] \[\Rightarrow \,\,4{{m}^{2}}=5\] \[\Rightarrow \,\,m=\pm \,\frac{\sqrt{5}}{2}\]


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