InterviewSolution
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InterviewSolution
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Find the relation obtained by eliminating `theta` from the equations `x=a cos theta+b sin theta` and `y=a sin theta- b sin theta`. |
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Answer» Given, `x=a cos theta + b sin theta ` `x^(2)=(a cos theta + b sin theta )^(2)` `=a^(2)cos^(2)theta+b^(2)sin^(2)theta+2ab cos theta sin theta ` Also `y=a sin theta - b cos theta` `y^(2)=a^(2)sin^(2)theta+b^(2)cos^(2) theta-2 ab sin theta cos theta ` `x^(2)+y^(2)=a^(2)(sin^(2) theta + cos^(2) theta)+b^(2)(cos^(2)theta+sin^(2) theta )` `=a^(2)+b^(2)` Hence, the required relation is `x^(2)+y^(2)=a^(2)+b^(2)`. |
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