I f space x equals space a sin t minus b cos t comma space y equals space a cos t plus space b sin t comma space space p r o v e space t h a t space fraction numerator d squared y over denominator d x squared end fraction equals fraction numerator minus open parentheses x squared plus space y squared close parentheses over denominator y cubed end fraction

Asked by inderjeet.saluja | 24th Aug, 2014, 05:38: PM

Expert Answer:

G i v e n x equals a sin space t space minus space b cos space t y equals a cos space t plus b sin space t fraction numerator d x over denominator d t end fraction equals a cos space t space plus b sin space t fraction numerator d y over denominator d t end fraction equals minus a sin space t plus b cos space t equals minus x fraction numerator d y over denominator d x end fraction equals fraction numerator d y over denominator d t end fraction cross times fraction numerator d t over denominator d x end fraction equals open parentheses minus a sin space t plus b cos space t close parentheses cross times fraction numerator 1 over denominator a cos space t space plus b sin space t end fraction fraction numerator d y over denominator d x end fraction equals fraction numerator minus a sin space t plus b cos space t over denominator a cos space t space plus b sin space t end fraction equals fraction numerator minus a sin space t plus b cos space t over denominator y end fraction fraction numerator d squared y over denominator d x squared end fraction equals fraction numerator d over denominator d x end fraction open parentheses fraction numerator d y over denominator d x end fraction close parentheses equals fraction numerator d over denominator d x end fraction open parentheses fraction numerator minus a sin space t plus b cos space t over denominator y end fraction close parentheses equals fraction numerator d over denominator d t end fraction open parentheses fraction numerator minus a sin space t plus b cos space t over denominator y end fraction close parentheses cross times fraction numerator d t over denominator d x end fraction  fraction numerator d over denominator d t end fraction open parentheses fraction numerator minus a sin space t plus b cos space t over denominator y end fraction close parentheses cross times fraction numerator d t over denominator d x end fraction equals fraction numerator y open parentheses minus a cos space t minus b sin space t close parentheses minus open parentheses minus a sin space t plus b cos space t close parentheses cross times begin display style fraction numerator d y over denominator d t end fraction end style over denominator y squared end fraction cross times open parentheses 1 over y close parentheses  fraction numerator d squared y over denominator d x squared end fraction equals fraction numerator minus y squared minus open parentheses minus x close parentheses squared over denominator y cubed end fraction equals fraction numerator minus open parentheses x squared plus y squared close parentheses over denominator y cubed end fraction  H e n c e space P r o v e d

Answered by Dharma Teja | 25th Aug, 2014, 09:41: AM

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