The length of the chord joining the points $\left( {4\cos {\rm{\theta }},\,\,4\sin {\rm{\theta }}} \right)$ and $\left( {4\cos \left( {{\rm{\theta }} + {{60}^0}} \right),4\sin \left( {{\rm{\theta }} + {{60}^0}} \right)} \right)$ of the circle ${x^2} + {y^2} = 16$ is

JEE MATHEMATICS MCQ: CIRCLES

1 Easy

1 of 1

Application +4 | -1

The length of the chord joining the points

\left( {4\cos \mathrm{\theta },\,\,4\sin \mathrm{\theta }} \right)

and

\left( {4\cos \left( {\mathrm{\theta } + {{60}^0}} \right),4\sin \left( {\mathrm{\theta } + {{60}^0}} \right)} \right)

of the circle

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

View answer and explanation

Correct option: A

Option A (4) is correct because the length of the chord is calculated to be 4 using trigonometric identities and the distance formula.

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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