InterviewSolution
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InterviewSolution
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If (x,y) and (X,Y) be the coordinates of the same point referred to two sets of rectangular axes with the same origin and if ax+by becomes pX+qY, where a,b are independent of x,y, thenA. `a^(2)-b^(2)=p^(2)-q^(2)`B. `a^(2)+b^(2)=p^(2)+q^(2)`C. `a^(2)+p^(2)=b^(2)+q^(2)`D. `a^(2)b^(2)=p^(2)q^(2)` |
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Answer» Correct Answer - B Suppose one set of rectangular axes is obtained by rotating the coordinate axes of the other set by an angle `theta` in anticlocwise sense. Let (x,y) be the coordinates of the point with respect to odd axes and (X,Y) be the coordinates with respect to the axes. then, `x=X cos theta-Y=X sin theta cos theta`, `:. ax+by=a(Xcos theta-Y sin theta) +b ( X sin theta+Y cos theta)` `rArr ax+by=(a cos theta+bsintheta) X+(b cos theta-sin theta)Y` It is given that `ax+by` becomes pX+qY `:. P=acos theta+b sin theta and q=b cos theta-a sin theta` `rArr p^(2)+q^(2)=(a cos theta+b sin theta)^(2)+ ( b sin theta- a sin theta)` `rArr p^(2)+q^(2)=a^(2)+b^(2)` |
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