Janna secondary student Hi! I have two questions involving locuses.Here's the first one: A point P moves such that it is always equidistant from the point G(2,5) and the line defined by y=3. Find the equation of the locus. I got as far as the equation: 3y2 -4y = -x2 + 4x - 16 and didn't know what to do from there. Of, course that whole equation could be wrong. Question 2: P is always twice as far from A(8,0) as it is from B(2,0). Find the equation of the locus. Once again, I got as far as y2 = -x2 -8x -56, and got stuck. Thanks for your help! Hi Janna, For your first problem, the distance from the point (x,y) to the line y = 3 is the "vertical" distance from the point to the line. This is the difference between y and 3, that is |y - 3|. The distance from (x,y) to (2,5) is the square root of (x - 2)2 + (y - 5)2. If the point (x,y) is on the locus then these two quantities are equal. Thus |y - 3| = SQRT[(x - 2)2 + (y - 5)2] Squaring both sides gives (y - 3)2 = (x - 2)2 + (y - 5)2 Expand and simplify. For the second problem I think that I can see where you made an error. If (x,y) is on the locus then Distance[(x,y) to (0,8)] = 2 Distance[(x,y) to (0,2)] That is SQRT[x2 + (y - 8)2] = 2 SQRT[x2 + (y - 2)2] Squaring both sides gives x2 + (y - 8)2 = 4 [x2 + (y - 2)2] Again, expand and simplify. Cheers, Harley Go to Math Central