A) 4
B) - 4
C) ± 4
D) None of these
Correct Answer: A
Solution :
Given that \[2y\,\,\cos \theta =x\,\sin \theta \] ?..(i) and \[2x\,\sec \theta -y\,\,\text{cosec}\,\theta =3\] ?..(ii) \[\Rightarrow \,\,\frac{2x}{\cos \theta }-\frac{y}{\sin \theta }=3\] \[\Rightarrow \,\,2x\,\sin \theta -y\,\cos \theta -3\,\sin \theta \cos \theta =0\] ?..(iii) Solving (i) and (iii), we get \[y=\sin \theta \] and \[x=2\,\,\cos \theta \] Now, \[{{x}^{2}}+4{{y}^{2}}=4\,\,{{\cos }^{2}}\theta +4\,\,{{\sin }^{2}}\theta \] \[=4\,({{\cos }^{2}}\theta +{{\sin }^{2}}\theta )=4\].
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