JEE Main & Advanced Sample Paper JEE Main Sample Paper-26

  • question_answer
    A chord PQ is a normal to the parabola \[{{y}^{2}}=4ax\] at P and subtends a right angle at the vertex. If \[SQ=\lambda \,SP\] where S is the focus then the value of \[\lambda \] is

    A)  1                    

    B)  2

    C)  3                                

    D)  4

    Correct Answer: C

    Solution :

    We have, \[\frac{2}{{{t}_{1}}}.\,\frac{2}{{{t}_{2}}}\,=-1\,\Rightarrow \,{{t}_{1}}{{t}_{2}}\,=-4;\] Also, \[{{t}_{2}}=-{{t}_{1}}-\frac{2}{{{t}_{1}}}\] \[{{t}_{1}}{{t}_{2}}\,=-t_{1}^{2}-2\Rightarrow \,-4+2=-t_{1}^{2}\Rightarrow \,t_{1}^{2}=2\] Also \[t_{2}^{2}\,=t_{1}^{2}\,+\frac{4}{t_{1}^{2}}+4\,\] squaring (1) \[\Rightarrow \,\,t_{2}^{2}=2+2+4=8\] \[SQ=a(1+t_{2}^{2})\,=a(1+8)=9a\] \[SP=a(1+t_{1}^{2}\,)=a(1+2)=3a\] \[\therefore \,\,\frac{SQ}{SP}=3\Rightarrow \,SQ=3SP\Rightarrow \,\lambda =3\]

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