# Get help with parametric equations

Recent questions in Parametric equations
Parametric equations

### Sketch the vector field F by drawing a diagram. $$\displaystyle{F}{\left({x},{y}\right)}={\frac{{{y}{i}+{x}{j}}}{{{\left({x}^{{{2}}}+{y}^{{{2}}}\right)}^{{{\frac{{{1}}}{{{2}}}}}}}}}$$

Parametric equations

### Find the area of the region that lies inside both curves. $$\displaystyle{r}=\sqrt{{3}}{\cos{\theta}},{r}={\sin{\theta}}$$

Parametric equations

### Find sets of parametric equations and symmetric equations of the line that passes through the given point and is parallel to the given vector or line. (For each line, write the direction numbers as integers.) Point: (-3, 4, 5) Parallel to: $$\displaystyle\frac{{{x}-{1}}}{{2}}=\frac{{{y}+{1}}}{ -{{3}}}={z}-{5}$$ (a) Parametric equations (b) Symmetric equations

Parametric equations

### Replace the Cartesian equation with equivalent polar equations. x = 7

Parametric equations

### Given the points (2,6) and (6,10), find at least three equations from exponential function that pass through these point

Parametric equations

### For the given polar equation, write an equivalent rectangular equation $$\displaystyle{r}{\cos{\theta}}={13}$$

Parametric equations

### Replace the polar equations with equivalent Cartesian equations. Then describe or identify the graph. $$\displaystyle{r}^{{{2}}}=-{4}{r}{\cos{\theta}}$$

Parametric equations

### Convert the point from rectangular coordinates to spherical coordinates. $$\displaystyle{\left(-{3},-{3},\sqrt{{{2}}}\right)}$$

Parametric equations

### Find parametric equations for x, y, and z in terms of the polar coordinates r and $$\displaystyle\theta$$ to determine the points on the portion of the paraboloid x + y + z = 5 that is on or above the plane z=4

Parametric equations

### Find the length of the parametric curve defined over the given interval $$\displaystyle{x}={3}{t}-{6},{y}={6}{t}+{1},{0}\le{t}\le{1}$$

Parametric equations

### A vector-valued function $$r(t)$$ with its defining parametric equations is given by the following. $$x = f(t)$$ $$y = g(t)$$ $$r(t) = ft(i) + g(t)j$$ Now find the vector-valued function $$r(t)$$ with the given parametric equations.

Parametric equations

### Polar coordinates of point P are given. Find all of its polar coordinates. $$\displaystyle{P}={\left({1},-\frac{\pi}{{4}}\right)}$$

Parametric equations

### Find the area of the largest rectangle that can be inscribed in the ellipse $$\displaystyle{\frac{{{x}^{{{2}}}}}{{{a}^{{{2}}}}}}+{\frac{{{y}^{{{2}}}}}{{{b}^{{{2}}}}}}={1}$$

Parametric equations

### Surface s is a part of the paraboloid $$\displaystyle{z}={4}-{x}^{{2}}-{y}^{{2}}$$ that lies above the plane $$z=0$$.$$(6+7+7=20pt)$$ a) Find the parametric equation $$\displaystyle\vec{{r}}{\left({u},{v}\right)}$$ of the surface with polar coordinates $$\displaystyle{x}={u}{\cos{{\left({v}\right)}}},{y}={u}{\sin{{\left({v}\right)}}}$$ and find the domain D for u and v. b) Find $$\displaystyle\vec{{r}}_{{u}},\vec{{r}}_{{v}},$$ and $$\displaystyle\vec{{r}}_{{u}}\cdot\vec{{r}}_{{v}}$$. c) Find the area of the surface

Parametric equations

### Determine the x-y coordinates of the points where the following parametric equations will have horizontal or vertical tangents $$\displaystyle{x}={t}^{{3}}-{3}{t}$$ $$\displaystyle{y}={3}{t}^{{2}}-{9}$$

Parametric equations

### Express the point with cartesian coordinates Q(3,-1) in polar form

Parametric equations

### $$x = t− \sin t$$ $$y = 1 − \cos t −$$ curve given by the parametric equation $$\displaystyle=\frac{\pi}{{3}}$$ in point Find the equation of the tangent line

Parametric equations

### Write the equation of the line tangent to $$\displaystyle{f{{\left({x}\right)}}}={\tan{{x}}}+{3}$$ at $$\displaystyle{\left(\frac{\pi}{{4}}.{4}\right)}$$

Parametric equations