A) \[mn\]
B) \[m{{n}^{2}}\]
C) \[1\]
D) \[{{m}^{2}}{{n}^{2}}\]
Correct Answer: D
Solution :
(d): \[x=m\sin \theta \] \[\Rightarrow \] \[{{x}^{2}}={{m}^{2}}{{\sin }^{2}}\theta \] \[y=n\cos \theta \] \[\Rightarrow \] \[{{y}^{2}}={{n}^{2}}{{\cos }^{2}}\theta \] \[{{n}^{2}}{{x}^{2}}={{m}^{2}}{{n}^{2}}{{\sin }^{2}}\theta \]__________(1) \[{{m}^{2}}{{y}^{2}}={{m}^{2}}{{y}^{2}}{{\cos }^{2}}\theta \]_________(2) \[\therefore \] \[{{n}^{2}}{{x}^{2}}+{{m}^{2}}{{y}^{2}}={{m}^{2}}{{n}^{2}}\]
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