Question

A set of points is such that each point is three times as far away from the y-axis as it is from the point (4,0).Then locus of the points is:

Answer 1

Let `(h,k)` is the point that is 3 times as far away from `y`-axis as it is from the point (4,0).
Then,
`h = 3sqrt((h-4)^2+k^2)`
`=>h^2 = 9(h^2+16-8h)+k^2`
`=>8h^2-72h+k^2+144 - 0`
`=>8(h^2-9h+81/4-81/4)+k^2 = -144`
`=>8(h-9/2)^2+k^2 = 162-144`
`=>8(h-9/2)^2+k^2 = 18`
`=>(h-9/2)^2/(9/4)+k^2/18 = 1`
If, we replace `(h,k)` by `(x,y)`, we can see that this is an equation for ellipse.