14. - / 0.81 points\nconsider the following.\n$x = \\tan^{2}(\\theta)$, $y = \\sec(\\theta)$, $-\\pi/2 <…

14. - / 0.81 points\nconsider the following.\n$x = \\tan^{2}(\\theta)$, $y = \\sec(\\theta)$, $-\\pi/2 < \\theta < \\pi/2$\n(a) eliminate the parameter to find a cartesian equation of the curve.\n(b) sketch the curve and indicate with an arrow the direction in which the curve is traced as the parameter increases.

14. - / 0.81 points\nconsider the following.\n$x = \\tan^{2}(\\theta)$, $y = \\sec(\\theta)$, $-\\pi/2 < \\theta < \\pi/2$\n(a) eliminate the parameter to find a cartesian equation of the curve.\n(b) sketch the curve and indicate with an arrow the direction in which the curve is traced as the parameter increases.

Answer

Explanation:

Step1: Recall the trigonometric identity

We know the identity (1+\tan^{2}\theta=\sec^{2}\theta).

Step2: Substitute the given parametric equations

Given (x = \tan^{2}\theta) and (y=\sec\theta). Substitute into the identity: (1 + x=y^{2}).

Step3: Consider the domain of (y)

Since (-\frac{\pi}{2}<\theta<\frac{\pi}{2}), (\sec\theta=y> 0).

Answer:

(y^{2}-x = 1,y>0)