A) \[\frac{64}{5}\]
B) \[\frac{52}{5}\]
C) \[\frac{56}{5}\]
D) \[\frac{32}{5}\]
Correct Answer: A
Solution :
[a] Equation of chord of contact is \[x\cdot 0+y\cdot 0-4(x+0)-2(y+0)+16=0\] \[\therefore \,\,\,\,\,\,2x+y-8=0\] \[\therefore \] Length of \[CM=\left[ \frac{2\cdot 4+2-8}{\sqrt{{{2}^{2}}+{{1}^{2}}}} \right]=\frac{2}{\sqrt{5}}\] units. \[\therefore \,\,\,AM=BM=\sqrt{4-\frac{4}{5}}=\sqrt{\frac{16}{5}}\] \[\therefore \] Length of chord of contact (AB) \[=\frac{8}{\sqrt{5}}\] \[\therefore \] Square of length of chord of Contact\[={{\left( \frac{8}{\sqrt{5}} \right)}^{2}}=\frac{64}{5}\].You need to login to perform this action.
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