The line joining $(5,0)$ to $(10 \cos \theta, 12 \sin \theta)$ is divided internally in the ratio $2: 3$ at $P$. If $\theta$ varies, then the locus of $P$ is

JEE MATHEMATICS MCQ: CIRCLES

1 Easy

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Application +4 | -1

The line joining

(5,0)

(10 \cos \theta, 12 \sin \theta)

is divided internally in the ratio

2: 3

P

. If

\theta

varies, then the locus of

P

View answer and explanation

Correct option: B

a circle

Option B (a circle) is correct because the locus of point P is derived to be a circle equation.

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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