JEE MAIN - Mathematics (2017 - 9th April Morning Slot - No. 21)
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 :
53
56
74
65
Explanation
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
$$ \therefore $$ 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
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