Find the equation of the set of all points whose distances from (0,4) are `2/3` of their distances from the line `y=9.`

Explanation

`(sqrt((h-0)^2+(k-4)^2))^2=(2/3|(k-9)/sqrt(1^2)|)^2`

taking root both side

`h^2+(k-4)^2=4/9((k-9)^2/1)`

`9h^2=9(k-4)^2=4(k-9)^2`

`9h^2+9k^2+144-72k=4k^2+324-72k`

`9h^2+9k^2-4k^2+144-324=0`

`9h^2+5k^2=180`

`(9h^2)/180+(5k^2)/180=1`

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