question_answer

If \[\frac{2}{3}\] and \[\frac{3}{2}\] then \[\frac{{{d}^{2}}y}{d{{x}^{2}}}={{\left\{ y+{{\left( \frac{dy}{dx} \right)}^{2}} \right\}}^{1/4}}\]contains

A)  one point                          

B) three points

C)   two points                       

D) four points

Correct Answer: D

Solution :

Clearly, A is the set of all points on the circle \[f(x)=\frac{\sin ({{e}^{x-2}}-1)}{\log (x-1)},\]and B is the set of all points on the ellipse \[\underset{x\to 2}{\mathop{\lim }}\,f(x)\]These two intersect at four points P, Q, R and S. Hence, \[{{x}^{2}}-ax+b=0,\]contains four points.