A line drawn through the point P(4, 7) cuts the circle x ^ 2 + y ^...

A line drawn through the point $

P\left(4, 7\right)

cuts the circle

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

at the points

A and

. Then

{P}_{A} \cdot {P}_{B}$ is equal to. 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

Options

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

Correct answer

C. $56$

Step-by-step solution

As we know,

\begin{array}{ll}PA . PB = P{T}^{2} = {S}_{1}^{2} \\ {S}_{1} = \sqrt{16 + 49 - 9} = \sqrt{56} \\ ⇒ {S}_{1}^{2} = 56 \\ ⇒ PA . PB = 56\end{array}

Practice Circle on Quantrex Academy →

More from Circle

Match each entry in List-I to the correct entry in List-II and choose the correct option.… JEE Advanced 2026 Consider the circle C: x^2+y^2-6x-8y-11=0 . Let a variable chord AB of the circle C… JEE Main 2026 Let C be a circle having centre in the first quadrant and touching the x -axis at a… JEE Main 2026 Let the line x - y = 4 intersect the circle C: (x-4)^2 + (y+3)^2 = 9 at the points Q and… JEE Main 2026 Let the centre of the circle x^2 + y^2 + 2gx + 2fy + 25 = 0 be in the first quadrant and… JEE Main 2026 Let P be a moving point on the circle x^2 + y^2 - 6x - 8y + 21 = 0 . Then, the maximum… JEE Main 2026 Suppose that two chords, drawn from the point (1, 2) on the circle x^2 + y^2 + x - 3y = 0… JEE Main 2026 Let a circle pass through the origin and its centre be the point of intersection of two… JEE Main 2026 Let a circle C have its centre in the first quadrant, intersect the coordinate axes at… JEE Main 2026 Let the circle x^ 2 +y^ 2 =4 intersect x -axis at the points A(a, 0), a>0 and B(b, 0) .… JEE Main 2026 Let y=x be the equation of a chord of the circle C_ 1 (in the closed half-plane x ≥ 0 )… JEE Main 2026 Let S=\ z ∈ ℂ:|(z-6 i)/(z-2 i)|=1. and .|(z-8+2 i)/(z+2 i)|=(3)/(5)\ . Then ∑_ z ∈ ~s… JEE Main 2026 Let a circle of radius 4 pass through the origin O, the points A(- 3 a, 0) and B(0,- 2 b)… JEE Main 2026 If the points of intersection of the ellipses x^ 2 +2 y^ 2 -6 x-12 y+23=0 and 4 x^ 2 +2… JEE Main 2026 Let the set of all values of r , for which the circles (x+1)^ 2 +(y+4)^ 2 =r^ 2 and x^ 2… JEE Main 2026 If P is a point on the circle x^ 2 +y^ 2 =4, Q is a point on the straight line 5 x+y+2=0… JEE Main 2026 Full Circle list Circle JEE Maths PYQs JEE Mathematics PYQs All JEE Main PYQs