A) Statement-1 is false, Statement-2 is true.
B) Statement-1 is true, statement-2 is true; statement-2 is a correct explanation for Statement-1.
C) Statement-1 is true, statement-2 is true; statement-2 is not a correct explanation for Statement-1.
D) Statement-1 is true, statement-2 is false.
Correct Answer: B
Solution :
Equation of tangent to the ellipse \[\frac{{{x}^{2}}}{2}+\frac{{{y}^{2}}}{4}=1\] is \[y=mx\pm \sqrt{2{{m}^{2}}+4}\] ..... (1) equation of tangent to the parabola \[{{y}^{2}}=16\sqrt{3}x\] is \[y=m\,x+\frac{4\sqrt{3}}{m}\] ..... (1) On comparing (a) and (2) \[\frac{4\sqrt{3}}{m}=\pm \sqrt{2{{m}^{2}}+4}\] \[\Rightarrow \,48={{m}^{2}}(2{{m}^{2}}+4)\] \[\Rightarrow 2{{m}^{4}}+4{{m}^{2}}-48=0\]\[\Rightarrow \,{{m}^{4}}+2{{m}^{2}}-24=0\] \[\Rightarrow ({{m}^{2}}+6)({{m}^{2}}-4)=0\]\[\Rightarrow {{m}^{2}}=4\] \[\Rightarrow m=\pm 2\] \[\Rightarrow \] equation of common tangents are \[y\pm 2x\pm 2\sqrt{3}\] statement -1 is true. statement-2 is obviously true.
You need to login to perform this action.
You will be redirected in
3 sec
