A) \[{{90}^{o}}\]
B) \[{{60}^{o}}\]
C) \[{{30}^{o}}\]
D) \[{{45}^{o}}\]
Correct Answer: A
Solution :
Let \[S={{y}^{2}}-12x\] Equation of pair of tangents is \[S{{S}_{1}}={{T}^{2}}\] \[\Rightarrow \] \[({{y}^{2}}-12x)[{{(2)}^{2}}-12(-3)]\] \[={{[y(2)-6(x-3)]}^{2}}\] \[\Rightarrow \] \[({{y}^{2}}-12x)(40)=4{{(y-3x+9)}^{2}}\] \[\Rightarrow \] \[10{{y}^{2}}-120x\] \[={{y}^{2}}+9{{x}^{2}}+81-6yx-54x+18y\] \[\Rightarrow \] \[9{{x}^{2}}-9{{y}^{2}}-6xy+66x+18y+81=0\] Here, \[a=9,\] \[b=-9\] \[\therefore \] \[a+b=0\] Hence, angle between tangents is \[{{90}^{o}}\].
You need to login to perform this action.
You will be redirected in
3 sec
