Polar equations of conics and rotation of axes

Use this for “Name the conic r = 4 ÷ (1 + sin θ), its eccentricity and its directrix.”

Use this for “For r = 3 ÷ (1 − 0.5 cos θ), find the vertices, the center and the lengths of the axes.”

Use this for “Find the vertex and the directrix of r = 4 ÷ (1 − cos θ), and the point at θ = 90°.”

Use this for “Through what angle should the axes turn to remove the xy term of 4x² + 2xy + 2y² = 1? Which conic is it?”

Use this for “Turn the axes to remove the xy term of 4x² + 2xy + 2y² = 1 and write the equation in x′ and y′.”