SOLUTION: what is an equation of the locus of points whose sum of the distances from any point on the conic to (-2,2) and (8,2) is 12?

Question 881785: what is an equation of the locus of points whose sum of the distances from any point on the conic to (-2,2) and (8,2) is 12?
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
This is a ellipse. The Distance Formula gives you a starting equation which with lengthy steps, and great attention to details, you can simplify.

You will want to subtract one of the radicals from both sides before squaring both sides, or your next steps can be extremely inconvenient. You will also need to square a second time.

Let me skip MOST of the steps here, and I will bring to the first form of the quadratic, conic section equation:

, requiring completing the square for x;

Not yet in standard form, but you can finish doing that.
RELATED QUESTIONS
Find the equation of the locus of a point which moves so that the sum of its distances... (answered by ikleyn)

please help find an equation of the locus of points the sum of whose distances from the... (answered by josgarithmetic)

We did not find results for: determine the equation of the ellipse such that the sum of... (answered by josgarithmetic)

"Find an equation of the locus of all points such that the difference of their distances... (answered by jsmallt9)

what is the general equation if the locus of a point which moves so that the sum of its... (answered by ikleyn,josgarithmetic)

Derive the equation of the locus of a point, the sum of the squares of whose distances... (answered by ikleyn)

The foci of an ellipse are (-3,-6) and (-3,2). For any point on the ellipse, the sum of... (answered by ikleyn)

I got this question on a test and i missed it its about locus of points... ther are 4 (answered by RAY100)

Please....help me solve this problem! Please! Find the equation of the locus of a... (answered by Alan3354)