A line drawn through the point P(4, 7) cuts the circle x2 + y2 = 9 at the points A and B.

Question

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

Accepted Answer

P(4, 7).   Here, x = 4, y = 7

$$ \therefore $$   PA $$ \times $$ PB = PT2

Also;   PT = $$\sqrt {{x^2} + {y^2} - {{\left( {x - y} \right)}^2}} $$

$$ \Rightarrow $$   PT = $$\sqrt {16 + 49 - 9} $$ = $$\sqrt {56} $$

$$ \Rightarrow $$   PT2 = 56

$$ \therefore $$   PA $$ \times $$ PB = 56

Solutions · 1