JEE MATHEMATICS MCQ: CIRCLES

1 Easy

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Application +4 | -1

If the radii of the circles

(x-1)^2+(y-2)^2=1

and

(x-7)^2+(y-10)^2=4

are increasing uniformly w.r.t. time as

0.3 \mathrm{\,unit} / \mathrm{s}

and

0.4 \mathrm{\,unit} / \mathrm{s}

respectively, then they will touch each other at

t

equals to

View answer and explanation

Correct option: B

90 \mathrm{~s}

Option B (90 s) is correct because it represents the time at which the distance between the centers equals the sum of the radii.

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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