11th Class Mathematics Conic Sections Question Bank Critical Thinking

  • question_answer Consider a circle with its centre lying on the focus of the parabola \[{{y}^{2}}=2px\] such that it touches the directrix of the parabola. Then, a point of intersection of the circle and the parabola is                           [IIT 1995]

    A)            \[\left( \frac{p}{2},\ p \right)\]

    B)            \[\left( \frac{p}{2},\ -p \right)\]

    C)            \[\left( \frac{-p}{2},\ p \right)\]      

    D)            \[\left( \frac{-p}{2},\ -p \right)\]

    Correct Answer: B

    Solution :

     Focus of parabola \[{{y}^{2}}=2px\] is                   \[(p/2,0)\]                                                         .....(i)                   \ Radius of circle whose centre is \[(p/2,0)\]and touching \[x+(p/2)=0\]is p.                   Equation of circle is \[{{\left( x-\frac{p}{2} \right)}^{2}}+{{y}^{2}}={{p}^{2}}\]     .....(ii)                    From (i) and (ii), we get the point of intersection \[\left( \frac{p}{2},p \right),\left( \frac{p}{2},-p \right)\].

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