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Grade: 12


A line is drawn through a fixed point P(α,β) to cut the circle x^2+y^2=r^2 at A and B. Then PA.PB is (α+β)^2-r^2 α^2+β^2-r^2 (α-β)^2+r^2 None of these

4 years ago

Answers : (2)

64 Points
when a line through a fixed point P cuts the circle in two different points A and B then PA.PB is called power of the point which is equal to S1
PA.PB =x12+y12-r2
                      = \small \alpha2+\small \beta2-r2      
    Hence, second option is correct .
4 years ago
ankit singh
522 Points

The equation of any line through the point P(α,β)
Any point on this line is
This point lies on the given circle, if
or k2+2kα+(αcosθ+βsinθ)+α2+β2r2=0.....(i)
Which being quadratic in k, gives two values of k
Let PA=k1, PB=k2, where k1,k2 are teh roots of Eq. (i) then

one month ago
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