Question

find the locus of a point whose distance from (0,4) is 2/3 times the distance from the line y-9=0. name the curve

Answer 1

step 1
let the moving point be (h,k)...

Answer 2

step 2
(use given statements)
distance of (h,k) from (0,4) which is sqrt((h-0)^2 +(k-4)^2)
and distance of (h,k) from the line y-9=0 is |k-9|

Answer 3

step3 condition(s)

Answer 4

sqrt((h-0)^2 +(k-4)^2) =2/3 ( |k-9|)

Answer 5

step4
change h to x and k to y and simplify further to get the required equation of the locus..

Answer 6

sqrt((x-0)^2 +(y-4)^2) =2/3 ( |y-9|)
squaring we have
x^2 + (y-4)^2 =4/9 (y-9)^2...

Answer 7

hope the steps are clear to you...

Answer 8

thank you @matricked

Answer 9

YW