To identify: The conic represented by the following polar equation and graph it by using the graphing utility: r=−4−1+cos⁡θ

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To identify:  The conic represented by the following polar equation and graph it by using the graphing utility:  r=−4−1+cos⁡θ

Clara Reese · Accepted Answer

Step 1 The conics sections of polar form r=ep1± ecos⁡θ or r=ep1± esin⁡θ are said to be: Parabola if e=1 Ellipse if e&amp;lt;1 Hyperbola if e&amp;gt;1 The given polar equation is: NKS r=−4−1+cos⁡θ Compared it with the standard equation of the polar form of a conic r=ep1± ecos⁡θ Get that: e=1 So, here the eccentricity is equal to one e=1, so the polar equation represents parabola. Hence, the given conic section (r=−4−1+cos⁡θ) is the parabola. For parabola: Vertex lies at (r, θ)=(2, π) with a horizontal axis. That means this parabola opens on upward direction. Now, confirm by using the graphing utility as:  From graph, it confirms that the graph represents a parabola. Thus the result verified successfully.

To identify: The conic represented by the following polar equation and

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