question_answer

Consider the parabolas \[{{S}_{1}}\equiv {{y}^{2}}-4ax=0\] and \[{{S}_{2}}\equiv {{y}^{2}}-4bx=0.\] \[{{S}_{2}}\] will contain \[{{S}_{1}},\] if

A) \[a>b>0\]

B) \[b>a>0\]

C) \[a>0,\,\,b<0\,\,but\,\,\left| \,b\, \right|>a\]

D) \[a<0,\,\,b>0\,\,but\,\,b>\left| \,a\, \right|\]

Correct Answer: B

Solution :

[b] If a and \[b>0\], then graphic representation would be as follows: \[{{S}_{2}}\] will contain \[{{S}_{1}},\] if latusrectum of \[{{S}_{2}}>\] latusrectum of \[{{S}_{1}}\] \[\Rightarrow 4b>4a\] \[\therefore \,\,\,\,\,b>a>0\]