Question

The ordinate of all points on the curve $y=\frac{1}{2{\sin }^{2}x+3{\cos }^{2}x}$ where the tangent is horizontal, is

• A. Always equal to $\frac{1}{2}$
• B. Always equal to $\frac{1}{3}$
• C. $\frac{1}{2}$ or $\frac{1}{3}$ according as $n$ is an even or an odd integer.
• D. $\frac{1}{2}$ or $\frac{1}{3}$ according as $n$ is an even integer

Answer 1

The correct option is C $\frac{1}{2}$ or $\frac{1}{3}$ according as $n$ is an even or an odd integer.

$y=\frac{1}{2si{n}^{2}x+3co{s}^{2}x}=\frac{1}{2+co{s}^{2}x}$

$tan\theta =\frac{dy}{dx}=\frac{-2sinxcosx}{(2+co{s}^{2}x{)}^2}=0$

$\therefore sinx=0$ or $cosx=0$

If $sinx=0,y=\frac{1}{3}$, if $cosx=0,y=\frac{1}{2}$