A) \[4+\sqrt{3}\]
B) \[\frac{12}{4-\sqrt{3}}\]
C) \[\frac{12}{4+\sqrt{3}}\]
D) \[\frac{-12}{4+\sqrt{3}}\]
Correct Answer: C
Solution :
\[{{x}^{2}}+{{y}^{2}}+xy-3=0\] | ? (1) | |
\[y=\frac{x}{\sqrt{3}}\] | ? (2) | |
\[\because \] centre of ellipse is (0, 0) and (2) also passes through (0, 0) | ||
\[\therefore \] chord will be bisect at (0, 0). | ||
\[\because \] Equation PQ is\[\frac{x-0}{\cos \frac{\pi }{6}}=\frac{y-0}{\sin \frac{\pi }{6}}=\pm \,r.\] | ||
\[\therefore \] \[\left( \frac{r\sqrt{3}}{2},\,\,\frac{r}{2} \right)\] lies on | ? (1) | |
\[\Rightarrow \] \[\frac{3{{r}^{2}}}{4}+\frac{{{r}^{2}}}{4}+\frac{{{r}^{2}}\sqrt{3}}{4}-3=0\] | ||
\[\Rightarrow \] \[{{r}^{2}}=\frac{3\times 4}{(4+\sqrt{3})}\] \[\Rightarrow \] \[{{r}^{2}}=\frac{12}{4+\sqrt{3}}\] | ||
\[\therefore \] \[|OP||OQ|\,\,=\frac{12}{4+\sqrt{3}}\] | ||
You need to login to perform this action.
You will be redirected in
3 sec