A) \[\frac{\sqrt{7}}{2}\]
B) \[\sqrt{\frac{5}{3}}\]
C) \[\sqrt{\frac{3}{2}}\]
D) \[\sqrt{2}\]
Correct Answer: C
Solution :
| Chord of contact w.r.t. \[(-\,4,\,\,2)\] is \[-\frac{4x}{{{a}^{2}}}-\frac{2y}{{{b}^{2}}}=1\] |
| Slope \[{{m}_{1}}=\frac{-\,2{{b}^{2}}}{{{a}^{2}}}\] ??(1) |
| Chord of contact w.r.t. (2, 1) is \[\frac{2x}{{{a}^{2}}}-\frac{y}{{{b}^{2}}}=1\] |
| Slope \[{{m}_{2}}=\frac{-2{{b}^{2}}}{{{a}^{2}}}\] |
| \[\therefore {{m}_{1}}{{m}_{2}}=-1\] |
| \[\frac{4{{b}^{4}}}{{{a}^{4}}}=1\] |
| \[2{{b}^{2}}={{a}^{2}}\] |
| \[\Rightarrow 2{{a}^{2}}({{e}^{2}}-1)={{a}^{2}}\] \[\Rightarrow e=\sqrt{\frac{3}{2}}\] |
You need to login to perform this action.
You will be redirected in
3 sec
