11th Class Mathematics Conic Sections Question Bank Critical Thinking

  • question_answer The equation of common tangents to the parabola \[{{y}^{2}}=8x\] and hyperbola \[3{{x}^{2}}-{{y}^{2}}=3\], is

    A)            \[2x\pm y+1=0\]                       

    B)            \[2x\pm y-1=0\]

    C)            \[x\pm 2y+1=0\]        

    D)            \[x\pm 2y-1=0\]

    Correct Answer: A

    Solution :

               Tangent to \[{{y}^{2}}=8x\]Þ \[y=mx+\frac{2}{m}\]            Tangent to \[\frac{{{x}^{2}}}{1}-\frac{{{y}^{2}}}{3}=1\]Þ\[y=mx\pm \sqrt{{{m}^{2}}-3}\]                   On comparing, we get                    m = ±2 or tangent as

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