JEE MATHEMATICS MCQ: CIRCLES

1 Easy

1 of 1

Application +4 | -1

P

is a point such that the ratio of the squares of the lengths of the tangents from

P

to the circles

{x^2} + {y^2} + 2x - 4y - 20 = 0

and

{x^2} + {y^2} - 4x + 2y - 44 = 0

2:3

, then the locus of

P

is a circle with centre

View answer and explanation

Correct option: B

\left( { - 7,8} \right)

Option B ((-7,8)) is correct because the locus of P is a circle with center (-7,8) after applying the given ratio condition.

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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