The locus of the moving point $ P $, such that $ 2 P A=3 P B $ where $ A $ is $ (0,0) $ and $ B $ is $ (4,-3) $, is

JEE MATHEMATICS MCQ: 2D GEOMETRY SYSTEM

1 Medium

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Application +4 | -1

The locus of the moving point

P

, such that

2 P A=3 P B

where

A

(0,0)

and

B

(4,-3)

, is

View answer and explanation

Correct option: D

5 x^{2}+5 y^{2}-72 x+54 y+225=0

Option D (

5 x^{2}+5 y^{2}-72 x+54 y+225=0

) is correct because it represents the locus of point P satisfying the given distance condition.

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\alpha

(\alpha, 2 \alpha)

\Delta A B C

A(0,2), B(2,0)

C(4,4)

(1, \sqrt{3}),(0,0)

(2,0)

(1,5),(-3,1) \,\&\,(-2,1)

9 x^2-16 y^2-18 x+32 y-23

=0

25 x^2+9 y^2-50 x-18 y+33=0

(0,0)(3,0)

(0,4)

A B C

A(-1,0), B\left(-2, \frac{3}{4}\right)

C\left(-3,-\frac{7}{6}\right)

H

B C H