A) \[{{y}^{2}}=2{{x}^{2}}\]
B) \[{{x}^{2}}=2{{y}^{2}}\]
C) \[{{x}^{2}}=4{{y}^{2}}\]
D) \[{{y}^{2}}=4{{x}^{2}}\]
Correct Answer: A
Solution :
(a): Radius of circle = r units In \[\Delta OCD,\angle COD={{90}^{{}^\circ }}\] \[\therefore \]\[C{{D}^{2}}=O{{C}^{2}}+O{{D}^{2}}\] \[\Rightarrow \]\[{{y}^{2}}={{r}^{2}}+{{r}^{2}}=2{{r}^{2}}\] .,..(i) In \[\Delta OAB\], \[OE\bot AB\] \[\angle OAB={{60}^{{}^\circ }}\] \[AE=\frac{x}{2}\] \[\therefore \]\[cos{{60}^{{}^\circ }}=\frac{AE}{OA}\] \[\Rightarrow \]\[\frac{1}{2}=\frac{\frac{x}{2}}{r}\] \[\Rightarrow \]\[\frac{1}{2}=\frac{x}{2r}\Rightarrow x=r\] ??(ii) From equations (i) and (ii), \[{{y}^{2}}=2{{x}^{2}}\]
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