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  • The tangent and normal at the point P(4, 4) to the parabola,   intersect the x–axis at the points

The tangent and normal at the point P(4, 4) to the parabola, y^2=4 x  intersect the x–axis at the points Q and R respectively. Then the cirucm centre of the ΔPQR is 

 

Option: 1

 (2, 0)


Option: 2

 (2, 1) 

 


Option: 3

 (1, 0)


Option: 4

 (1, 2) 

 


Answers (1)

best_answer

Eq. of tangent 2 y=x+4

\therefore \mathrm{Q} \equiv(-4,0)

Eq. of normal is    y-4=-2(x-4)

      

\Rightarrow y+2 x=12

Clearly QR is diameter of the required circle.

\begin{aligned} & \Rightarrow(\mathrm{x}+4)(\mathrm{x}-6)+\mathrm{y}^2=0 \\ & \Rightarrow \mathrm{x}^2+\mathrm{y}^2-2 \mathrm{x}-24=0 \\ & \text { centre }(1,0) \end{aligned}

Posted by

sudhir kumar

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