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  • Stuck here, help me understand: A line drawn through the point P(4, 7) cuts the circle x2+y2=9 at the points A and B. Then PA⋅PB is equal to :

 A line drawn through the point P(4, 7) cuts the circle x2+y2=9 at the points A and B. Then PA⋅PB is equal to :

  • Option 1)

    53

  • Option 2)

    56

  • Option 3)

    74

  • Option 4)

    65

 

Answers (1)

best_answer

As we learnt

 

Length of a tangent -

 

L=\sqrt{x{_{1}}^{2}+y{_{1}}^{2}+2gx_{1}+2fy_{1}+c}

 

- wherein

Length of tangent from a external point (x_{1},y_{1})  to circle x^{2}+y^{2}+2gx+2fy+c=0

 

 

Since we know,

PA.PB=PT^2

PT=\sqrt{4^2+7^2-9}

\Rightarrow PT^2= \left ( \sqrt{56} \right )^{2}= 56

 

 


Option 1)

53

Option 2)

56

Option 3)

74

Option 4)

65

Posted by

satyajeet

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