Question

(5,-4),(7,6) are in the ratio of 2:3 then find the locus of p please​

Answer 1

Answer:

Let the point P be (x,y)

The distance between the points (x,y),(2,3) is

(2−x)

2

+(3−y)

2

The distance between the points (x,y),(2,−3) is

(2−x)

2

+(−3−y)

2

Given that the distances are in the ratio of 2:3

Therefore,

(2−x)

2

+(−3−y)

2

(2−x)

2

+(3−y)

2

=

3

2

⟹

(2−x)

2

+(−3−y)

2

(2−x)

2

+(3−y)

2

=

9

4

⟹

4+x

2

−4x+9+y

2

+6y

4+x

2

−4x+9+y

2

−6y

=

9

4

⟹9(4+x

2

−4x+9+y

2

−6y)=4(4+x

2

−4x+9+y

2

+6y)

⟹36+9x

2

−36x+81+9y

2

−54y=16+4x

2

−16x+36+4y

2

+24y

⟹5x

2

+5y

2

−20x−78y+65=0

Therefore, the locus of the point P is 5x

2

+5y

2

−20x−78y+65=0

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