91Ó°ÊÓ

Finding a Derivative In Exercises \(1-4,\) find \(d y / d x\) $$ x=t^{2}, y=7-6 t $$

Graphical Reasoning In Exercises \(1-4,\) use a graphing utility to graph the polar equation when (a) \(e=1,\) (b) \(e=0.5,\) and \((\mathrm{c}) e=1.5 .\) Identify the conic. $$ r=\frac{2 e}{1+e \cos \theta} $$

Polar-to-Rectangular Conversion In Exercises \(1-10,\) plot the point in polar coordinates and find the corresponding rectangular coordinates for the point. $$ \left(8, \frac{\pi}{2}\right) $$

In Exercises 1–18, sketch the curve represented by the parametric equations (indicate the orientation of the curve), and write the corresponding rectangular equation by eliminating the parameter. $$ x=2 t-3, \quad y=3 t+1 $$

Graphical Reasoning In Exercises \(1-4,\) use a graphing utility to graph the polar equation when (a) \(e=1,\) (b) \(e=0.5,\) and \((\mathrm{c}) e=1.5 .\) Identify the conic. $$ r=\frac{2 e}{1-e \cos \theta} $$

Polar-to-Rectangular Conversion In Exercises \(1-10,\) plot the point in polar coordinates and find the corresponding rectangular coordinates for the point. $$ \left(-2, \frac{5 \pi}{3}\right) $$

In Exercises 1–18, sketch the curve represented by the parametric equations (indicate the orientation of the curve), and write the corresponding rectangular equation by eliminating the parameter. $$ x=5-4 t, \quad y=2+5 t $$

Finding a Derivative In Exercises \(1-4,\) find \(d y / d x\) $$ x=\sqrt[3]{t}, y=4-t $$

Polar-to-Rectangular Conversion In Exercises \(1-10,\) plot the point in polar coordinates and find the corresponding rectangular coordinates for the point. $$ \left(-4,-\frac{3 \pi}{4}\right) $$

Finding a Derivative In Exercises \(1-4,\) find \(d y / d x\) $$ x=\sin ^{2} \theta, y=\cos ^{2} \theta $$