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

Find the equation of the set of all points the sum of whose distance from the points `(3,0)a n d(9,0)` is `12.`

Text Solution

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Let the coordinates of the point be `(x,y)` then according to the question
`sqrt((x-3)^(3)+y^(2))+sqrt((x-9)^(2)+y^(2))=12`
`sqrt((x-3)^(3)+y^(2))=12-sqrt((x-9)^(2)+y^(2))`
On sqauring both sides we get
`x^(2)-6x+9+y^(2)=144+(x^(2)-18x+81+y^(2))-24sqrt((x-9)^(2)+y^(2))`
`rArr 12x-216=-24sqrt((x-9)^(2)+y^(2))`
`rArr x-18=-2sqrt((x-9)^(2)+y^(2))`
`rArr x^(2)-36x+324=4(x^(2)-18x+81+y^(2))`
`rArr3x^(2)+4y^(2)-36x=0`
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