A) \[\left( \frac{-7}{2},-4 \right)\]
B) \[\left( \frac{-18}{5},\frac{-21}{5} \right)\]
C) (2,-7)
D) (-2, -5)
Correct Answer: B
Solution :
Let point of contact be\[P({{x}_{1}},\ {{y}_{1}})\]. This point lies on line \[{{x}_{1}}+2{{y}_{1}}=-12\] ?. (i) Gradient of \[OP={{m}_{1}}=\frac{{{y}_{1}}-1}{{{x}_{1}}+1}\] Gradient of \[x+2y+12={{m}_{2}}=-\frac{1}{2}\] The two lines are perpendicular, \[\therefore \ {{m}_{1}}{{m}_{2}}=-1\] \[\Rightarrow \left( \frac{{{y}_{1}}-1}{{{x}_{1}}+1} \right)\text{ }\left( \frac{-1}{2} \right)=-1\Rightarrow {{y}_{1}}-1=2{{x}_{1}}+2\] \[\Rightarrow 2{{x}_{1}}-{{y}_{1}}=-3\] ?. (ii) On solving equation (i) and (ii), we get \[({{x}_{1}},\ {{y}_{1}})=\left( \frac{-18}{5},\ \frac{-21}{5} \right)\] .You need to login to perform this action.
You will be redirected in
3 sec