if P is a point on the y axis such that 4 times its distance from A(5,2) is equal to - Maths - Coordinate Geometry

Question

if P is a point on the y axis such that 4 times its distance from
A(5,2) is equal to twice itsdistance from B(8,8),then find its
coordinates

Rishabh Mittal · Accepted Answer

Dear Student ,

Please find below the solution to the asked query :

Let the point P be 0,y 
Now,4AP=2BP16AP2=4BP24AP2=BP245-02+2-y2=8-02+8-y24 25+4-4y+y2=64+64-16y+y2116-16y+4y2=128-16y+y24y2-y2=128-1163y2=12y2=4y=±2So , Point P is 0,2 or 0,-2 
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if P is a point on the y axis such that 4 times its distance from A(5,2) is equal to twice itsdistance from B(8,8),then find its coordinates.