1.Graph the coordinate then name the three other pairs of polar coordinates for P (−2,π/4)
2.Rewrite in polar form: x^2 + y^2 − 2y = 7
3.Rewrite in rectangular form: r = 6 cos θ
4.Sketch the graph of: r = 6 sin θ. What is the shape, radius and center?
5.Which conic section is represented by r =6/3−4 cos θ? What is its eccentricity, orientation and directrex?
As an AI language model, I cannot produce visual content, however, I will provide textual answers to the questions:
1. The polar coordinate of P (-2, π/4) can be represented as (2, 5π/4), (2, -3π/4), and (-2, 3π/4).
2. The equation x^2 + y^2 - 2y = 7 can be rewritten in polar form as r^2 - 2rsinθ = 7.
3. The equation r = 6 cosθ can be rewritten in rectangular form as x = 6cosθ and y = 6sinθ.
4. The graph of r = 6sinθ is a circle with radius 3 units and center at the origin.
5. The conic section represented by r = 6/3 - 4cosθ is an ellipse with eccentricity 2/3, orientation parallel to the x-axis, and the directrix at y = -4/3.