Find the equation of the locus of a point which moves such that theratio of its distances from `(2,0)a n d(1,3)`is `5: 4.`

Find the equation of the locus of a point which moves such that therat

1.	Find the equation of the locus of a point which moves such that theratio of its distances from `(2,0)a n d(1,3)`is `5: 4.`
Answer» `(AP)/(BP)=5/4` `(AP)^2/(BP)^2=(25/16)``d=sqrt((x_1-x_2)^2+(y_1-y_2)^2` `d^2=(x_1-x_2)^2+(y_1-y_2)^2` `(AP)^2=(h-2)^2+(k-0)` `(BP)^2=(h-1)^2+(k-3)^2` `(AP)^2/(BP)^2=25/16` `((h-2)^2+k^2)/((h-1)^2+(k-3)^2)=25/16` `16h^2+64-64h+16k^2=25h^2+25-50h+25k^2+225-150h` `9h^2+9k^2+14h-150k+186=0` Putting h=x,k=y `9x^2+9y^2+14x-150y+186=0`.

A point moves so that the sum of its distances from `(a e ,0)a n d(-a e ,0)`is `2a ,`prove that the equation to its locus is `(x^2)/(a^2)+(y^2)/(b^2)=1`, where `b^2=a^2(1-e^2)dot`
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Find the equation of the locus of a point which moves such that theratio of its distances from `(2,0)a n d(1,3)`is `5: 4.`
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