A line drawn through the point P 4 , 7 cuts the circle x 2 + y 2 = 9 at the points A and B . Then P A · P B is equal to.

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Question: Answered & Verified by Expert

A line drawn through the point

P (4, 7)

cuts the circle

x^{2} + y^{2} = 9

at the points

A

and

B

. Then

P_{A} \cdot P_{B}

is equal to.

MathematicsCircleJEE MainJEE Main 2017 (09 Apr Online)

Options:

A $74$
B $53$
C $56$
D $65$

Solution:

2218 Upvotes Verified Answer

The correct answer is:

56

As we know,

\begin{array}{l} P A . P B = P T^{2} = S_{1}^{2} \\ S_{1} = \sqrt{16 + 49 - 9} = \sqrt{56} \\ \Rightarrow S_{1}^{2} = 56 \\ \Rightarrow P A . P B = 56 \end{array}

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