SOLUTION: find the equation of the set of all points such that the sum of the distances of P(x,y) from (0,-3) and (0,3) is equal to 10.

Question 62662: find the equation of the set of all points such that the sum of the distances of P(x,y) from (0,-3) and (0,3) is equal to 10.
Answer by uma(370) (Show Source): You can put this solution on YOUR website!
Distance between P(x,y) and (0,-3) is given by:
D^2 = (x-0)^2 + (y-(-3))^2
= x^2 + (y+3)^2
Likewise distance between P(x,y) and (0,3) is:
D1^2 = (x-0)^2 + (y-3)^2
= x^2 + (y-3)^2
Given that the sum of the distances = 10
==> x^2 + (y+3)^2 + x^2 + (y-3)^2 = 100
==> x^2 + y^2 + 6y + 9 + x^2 + y^2 - 6y + 9 = 100
==> 2x^2 + 2y^2 + 18 = 100
==> 2x^2 + 2y^2 = 100 - 18 [adding -18 to both the sides]
==> 2x^2 + 2y^2 = 82
==> x^2 + y^2 = 41
This is the required equation.
Good Luck!!!

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