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Find the equation of the set of all poin...

Find the equation of the set of all points whose distances from `(0,4)a r e2/3` of their distances from the line `y=9.`

Text Solution

Verified by Experts

Let the points be P(x,y)
`therefore` Distance from (0,4)=`sqrt(x^(2)+(y-4)^(2))`
So, the distance from the line y=9 is `abs((y-9)/1)`
`sqrt(x^(2)+(y-4)^(2))=2/3abs((y-9)/1)`
`rArr x^(2)+y^(2)-8y+10=4/9(y^(2)-18y+81)`
`rArr 9x^(2)+9y^(2)-72y+144=4y^(2)-72y+324`
`rArr 9x^(2)+5y^(2)=180`
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