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?

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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) About Me  (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.

sqrt%28%28x%2B2%29%5E2%2B%28y-2%29%5E2%29%2Bsqrt%28%28x-8%29%5E2%2B%28y-2%29%5E2%29=12
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:

11x%5E2-66x%2B36y%5E2=153, requiring completing the square for x;
11%28x%5E2-6x%2B9%29%2B36y%5E2=153%2B99
highlight_green%2811%28x-3%29%5E2%2B36y%5E2=162%29
Not yet in standard form, but you can finish doing that.