A point `P`moves in such a way that the ratio of its distance from two coplanarpoints is always a fixed number `(!=1)`. Then, identify the locus of the point.

A point `P`moves in such a way that the ratio of its distance from two

1.	A point `P`moves in such a way that the ratio of its distance from two coplanarpoints is always a fixed number `(!=1)`. Then, identify the locus of the point.
Answer» Let two coplanar points be A(0,0) and B9a,0). Let P(x,y) be the variable point. According to question, `(AP)/(BP)=lambda` `:. (sqrt(x^(2)+y^(2)))/(sqrt((x-a)^(2)+y^(2)))=lambda`, (where `lambda` is any fixed number and `lambda cancel(=)1)` or `x^(2)+y^(2)+((lambda^(2))/(lambda^(2)-1))(a^(2)-2ax)=0` which is the equation of a circle.

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A point `P`moves in such a way that the ratio of its distance from two coplanarpoints is always a fixed number `(!=1)`. Then, identify the locus of the point.

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