FAMILY OF CURVES

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1. Family of vertical parabolas whose vertex lies on the line y = -x. (Answer: 2yy" + 2xy" - (y')= - 2y' =0) 2. Family of unit circles centered at origin. (Answer x + yy' = 0) 3. Family of unit circles centered at (h, k). (Answer: (y')= - [1 + (y')=]= = 0) 4. Family of lines whose product of the intercepts is -1. (Answer: y'x + /y' - y = 0) 5. Family of horizontal parabolas whose h to k ratio is 2. (Answer: 2xy" - 4yy" -40)*+y' =0) 6. Family of circles centered at the line y = 2x. (Answer:y"(y - 2x) + 2073+ ()= + 2y' + 1 =0) 7. Family of circles centered at (h, k). (Answer: y'" [1 + (y))"] - 3y'(")3 =0)