A line through $P\left( {1,4} \right)$ intersect a circle ${x^2} + {y^2} = 16$ at $A$ and $B$, then $PA.PB$ is equal to

JEE MATHEMATICS MCQ: CIRCLES

1 Easy

1 of 1

Application +4 | -1

A line through

P\left( {1,4} \right)

intersect a circle

{x^2} + {y^2} = 16

A

and

B

, then

PA.PB

is equal to

View answer and explanation

Correct option: A

Option A (1) is correct because

PA.PB

is equal to the square of the length of the tangent from point

P

to the circle, which can be calculated using

PT^2 = S_1

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{\left( {{\alpha ^2}{x^2} - 2\alpha \mathrm{ }x + 1} \right)^{51}},

x

\left( {\alpha ,2{\alpha ^2}} \right)

{x^2} + {y^2} = 4,

{x^2} + {y^2} - 2x + 4y - 4 = 0

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

\left( {{x_1},{y_1}} \right)

\quad \alpha, \beta

\gamma

P, Q

x^2+y^2=1

A

(-1,0)

A P, A Q

A R

G P

\cos \alpha / 2, \cos \beta / 2

\cos \gamma / 2

x+y=6

x+2 y=4

x+y=5

x-y=1

9 \pi