Identify the conic section given by the polar equation displaystyle{r}=frac{4}{{{1}- cos{theta}}} and also determine its directrix.

Determine whether the statement, 'I noticed that depending on the values for A and C, assuming that they are not both zero, the graph of ${\displaystyle A{x}^2+C{y}^2+Dx+Ey+F=0}$ can represent any of the conic sections', makes sense or does not make sense, and explain your reasoning.

The rational exponent form of ${\displaystyle a^{0.4}}$ in radical form.

Find semi-major/semi-minor axis of ellipse from parametric equations with different phase
${\displaystyle x=\hat{x}\cdot \cos (\Omega t-\theta )}$
${\displaystyle y=\hat{y}\cdot \sin (\Omega t-\phi )}$

Given: ${\displaystyle y=x^{1.65}}$
Could it be described as parabolic in shape, or does the equation have to have ${\displaystyle x^2}$ as its highest degree term?

How do you name the curve given by the conic ${\displaystyle r=6}$?

Given the force field F, find the work required to move an object on the given oriented curve. ${\displaystyle F=⟨y,x⟩}$ on the parabola ${\displaystyle y=2x^2\mathfrak{o}mPSK(0,0)}$ to ${\displaystyle (2,8)}$

To calculate the verties and foci of the conic section: ${\displaystyle \left(x^9\right)2+\left(y^4\right)2=1}$