Gate Exam Programming Arrays

how to find differential eqn. of all conics whose axes coincide with coordinate axes??

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The sum of three positive real numbers x, y and z is 9. If the largest positive difference between any 2 of the 3 numbers is 5 and these 3 numbers are in arithmetic progression then the product of these 3 numbers will be what If the letters of the word are arranged as in dictionary, find the rank of the word INDIA.