To identify: The conic represented by the following polar equation and graph it by using the graphing utility: r=51−sin⁡θ

Question

To identify:  The conic represented by the following polar equation and graph it by using the graphing utility:  r=51−sin⁡θ

Elberte · 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=51−sin⁡θ Compared it with the standard equation of the polar form of a conic r=ep1± esin⁡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=51−sin⁡θ) is the parabola. For parabola: Vertex lies at (r, θ)=(2.5, 3π2) 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

Answered question

Answer & Explanation

New Questions in Integral Calculus