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JEE Mains · Maths · STD 11 - 10.1 circle and system of circle
A line drawn through the point \(P(4, 7)\) cuts the circle \(x^2 + y^2\, = 9\) at the points \(A\) and \(B\). Then \(PA· PB\) is equal to
- A \(53\)
- B \(56\)
- C \(74\)
- D \(65\)
Answer & Solution
Correct Answer
(B) \(56\)
Step-by-step Solution
Detailed explanation
\(P\left( {4,7} \right)\). Here, \(x = 4,y = 7\) \(x - y = - 3\) \(PA \times PB = P{T^2}\) \(P{T^2} = \sqrt {{x^2} + {y^2} - {{\left( {x - y} \right)}^2}} \) \(PT = \sqrt {16 + 49 - 9} = \sqrt {56} \) \(P{T^2} = 56;PA \times PB = 56\)
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